UC-NRLF 


OSBORN'S  TABLES. 


LIBRARY 

OF   THE 

UNIVERSITY  OF  CALIFORNIA. 
Class 


u 


0 


SBORN'S   TABLES 


OF 


MOMENTS  OF  INERTIA 

AND 

SQUARES  OF  RADII  OF  GYRATION 

TO   WHICH   HAVK   BEEN   ADDED   TABLES   OF 

THE  WORKING  STRENGTHS  OF  STEEL  COLUMNS, 

THE  WORKING  STRENGTHS  OF  TIMBER 
BEAMS  AND  COLUMNS, 

STANDARD    LOADS    AND    UNIT    STRESSES, 

AND  CONSTANTS  FOR  DETERMINING 
STRESSES  IN  SWING  BRIDGES. 


OF  THE 

UNIVERSITY 


FIFTH    EDITION 

REVISED  BY 

THE  OSBORN   ENGINEERING  CO. 

1905 


COPYRIGHT,    I9O5 

BY 

THE   OSBORN    ENGINEERING   COMPANY, 
CLEVELAND 


1 


PREFACE  TO  FIFTH  EDITION. 

"Osborn's  Tables"  are  now  too  well  known  among  engineers 
and  designers  to  require  further  introduction.  The  first  edition,  by 
Mr.  Frank  C.  Osborn,  appeared  in  1886,  and  was  followed  in  turn 
by  three  others  in  the  next  eight  years.  Since  the  publication  of 
the  fourth  edition  in  1894,  the  various  mills  have  adopted  uniform 
standards  of  shapes  which  nearly  all  varied  somewhat  from  those 
used  in  the  tables.  This  considerably  decreased  the  usefulness  of 
the  tables  as  they  then  existed. 

Believing,  however,  that  the  work  still  fills  a  want  among  de- 
signing engineers,  the  present  edition  has  been  prepared.  The 
tables  of  moments  of  inertia  and  squares  of  radii  of  gyration  have 
all  been  completely  refigured,  using  the  present  standard  mill  sec- 
tions and  shapes,  and  combining  them  in  accordance  with  present 
designing  practice.  It  is  believed  that  these  tables  will  prove  much 
more  convenient  than  the  earlier  ones  in  this  respect. 

The  tables  of  —  >  square  root,  swing  bridges,  rivets,  web  plates 
and  timber  beams,  have  alt  been  preserved  in  the  present  edition. 
Some  of  the  other  matter,  now  obsolete,  has  been  omitted  and 
instead  there  have  been  included  tables  of  the  safe  working 
strengths  of  soft  steel  and  medium  steel  columns,  of  standard  loads 
and  unit  stresses  for  bridges,  of  timber  columns  and  of  bridge 
weights. 

There  have  also  been  included  a  few  pages  of  historical  and 
other  statistics  concerning  the  bridges  of  the  world  that  it  is  hoped 
may  prove  of  interest.  Such  information  is  not  easily  obtainable 
elsewhere. 

It  is  earnestly  hoped  that  this  new  work  may  have  the  same 
kind  reception  and  may  prove  as  useful  a  companion  to  the  design- 
ing engineer  as  have  its  preceding  editions. 

THE  OSBORN  ENGINEERING  COMPANY. 
CLEVELAND,  MARCH,  1905. 


CONTENTS. 

Page 

Explanation 6 

Moments  of  Inertia,  Rectangles w 

Squares  of  Radii  of  Gyration,  Two  Angles 14 

*•       "       "     "          "          "          "       and  One  Top  Plate  18 
MOMENTS  OF  INERTIA  AND  SQUARES  OF  RADII  OF  GYRATION  : 

One  Web  Plate  and  Two  Angles 20 

One  Web  Plate,  Two  Angles  and  Top  Plate  ....  24 

Two  Web  Plates,  Two  Angles*  and  Top  Plate     ...  26 

Squares  of  Radii  of  Gyration,  Four  Angles 28 

MOMENTS  OF  INERTIA  AND  SQUARES  OF  RADII  AND  GYRATION: 

One  Web  Plate  and  Four  Angles 32 

Two  Web  Plates  and  Four  Angles 42 

Two  Web  Plates,  Two  Side  Plates  and  Four  Angles         .  50 

Three  I  Beams 53 

Two  Channels  and  One  Separating  I  Beam        ...  54 
Two  Web  Plates,  Four  Angles  and  Top  Plate        .        .        .58 

Two  Channels  and  One  Top  Plate 75 

Two  Web  Plates,  Two  Side  Plates,  Four  Angles 

and  Top  Plate 78 

Two  Web  Plates,  Four  Angles,  Top  Plate  and 

Horizontal  Flange  Plates 82 

Two  Web  Plates,  Two  Side  Plates,  Four  Angles, 

Top  Plate,  and  Horizontal  Flange  Plates           .       .  84 

Values  of  M. 86 

Working  Strengths  of  Soft  Steel  Columns           .                        .  97 

"                           "   Medium  Steel  Columns      .       .        .  100 

Square  Roots           .         .         . 103 


SWING  BRIDGES;  SHEARS  AND  MOMENTS: 
Three  Points  of  Support,  Single  I,oads, 

Spans  of  Four  to  Twenty  Panels    .        .        .        112  to  127 
Three  Points  of  Support,  Symmetrical  I«oads, 

Spans  of  Six  to  Twenty  Panels        ....    12810141 
Four  Points  of  Support,  Symmetrical  I«oads, 

Spans  of  Seven  to  Nineteen  Panels  .        .        142  to  153 

Bearing  and  Shearing  Values  of  Rivets 

per  Foot  Run 154 

Safe  Resistance  Against  Buckling  of  Girder  Webs  .  .  155 
Centrifugal  Force  in  Per  Cent,  of  Weight  ....  156 
Chords  I,oaded  Transversely  .  .  .  .  .  .  157 

Portal  Bracing  158 

Camber 160 

I«ength  of  Flange  Plates,  Girders 162 

Bending  Moments  for  Various  I^oads  and  Spans  .  .  .  163 
Capacity  of  Timber  Beams  :  800  Ibs.  to  1500  Ibs.  per 

square  inch  fibre  strain 164  to  167 

Timber,  Safe  Working  Stresses 168 

Timber  Columns,  Working  Strengths    .  ....    168 

Weights  of  Railway  Bridges 169 

Cooper's  Standard  goading  for  Railway  Bridges  .  .  .170 
The  Osborn  Engineering  Company's  Standard 

leading  for  Electric  Railway  Bridges  ...       171 

The  Osborn  Engineering  Company's  Standard 

loading  for  Highway  Bridges 172 

Impact  Formulae 173 

Unit  Stresses  I73 

Formulae  for  I  and  r^,  Carnegie  Shapes         ....        174 

Formulae  for  I  and  >-2,  Usual  Sections 175 

Conventional  Signs  for  Rivets  .  .....       176 

Bridges  :— Historical  and  Other  Data  177 


EXPLANATION. 

The  shapes  used  in  the  following  tables  are  those  manufactured 
by  the  Carnegie  Steel  Co.,  Pittsburg  Pa.  The  moments  of  inertia 
will  not,  however,  vary  materially  for  shapes  of  same  size  and 
weight  made  by  other  manufacturers. 

In  all  cases  calculations  have  been  based  on  the  gross  area,  and 
if  it  is  desired  to  use  the  sections  as  beams  to  resist  direct  bendingf 
due  allowance  should  be  made  for  loss  of  section  from  rivet  holes 
in  tension  flanges. 

The  following  example  will  illustrate  the  general  method  pur- 
sued in  obtaining  the  moment  of  inertia  and  square  of  radius  of  gy- 
ration for  sections  composed  of  two  plates  and  four  angles  riveted 
as  shown  on  page  43: 


2  plates  12  x  5^=6.00  sq.  ins. 
4  angles  3^  X  2%  X  %— 8.44 

Total,  14.44  sq.  ins. 


-HI2  X        122=   72.OO 

X  5-342=24o.7i 
4  X  1.09  —    4.36 

1=317.07 
317.07 + 14.44=21. 96=  ^2 

The  moment  of  inertia  of  the  plates  being  y1^  6d3=^!f  Ad*  in 
which  £=breadth,  tf=depth,  and  A  the  area  of  the  plates;  and 
the  moment  of  inertia  of  each  angle  being  adi+i,  in  which  a  equals 
the  area  of  the  angle,  d  the  distance  of  its  center  of  gravity  from 
the  neutral  axis  of  the  section,  and  z,  its  moment  of  inertia  about 
an  axis  through  its  own  center  of  gravity  parallel  to  that  neutral 
axis.  In  the  above  example,  5.34  inches  is  the  distance  from  center 
of  gravity  of  angle  to  the  neutral  axis,  and  1.09  is  the  moment  of 
inertia  of  one  angle  about  an  axis  through  its  center  of  gravity,  as 
given  in  Carnegie's  Pocket  Companion. 

For  trough-shaped  sections  it  is  convenient  to  first  determine 
the  position  of  the  neutral  axis,  which  is  done  as  follows;  Multiply 
the  area  of  the  top  plate,  top  angles,  webs  and  bottom  angles,  each 
by  the  distance  of  its  center  of  gravity  from  the  lower  edge  of  web. 
Divide  the  sum  of  these  products  by  the  total  area  of  the  section, 
and  the  result  will  be  the  distance  of  the  neutral  axis  above  the 
lower  edge  of  the  web: 


Top  plate  17  X  %=  6.38  X  14-19=  90.53 
2  top  angles  3  X  3  X  %==  4.22  X  13.11=  55.32 
2  web  plates  14  X  ^=10.50  X  7.oo«  73.50 
2  hot.  angles  4  X  3  X  SA=  7.96  X  0.87=-  6.92 

29.06  X    7.79=226.27 

7.00 
deduct,  29.06  X  0.792 


6.38  X  7-i92=3-9-S2 
4.22  X  6.112=157.54 
10.50-4-12X142=171.50 
7.96  X  6.132=299.11 

957-97 
+    9-36 

96733 
-     17.99 

1=949  34 
r  2 =949.34-1-  29.06-32. 7 

Find  the  moment  of  inertia  of  the  section  about  an  axis  through 
the  center  of  the  web,  as  follows:  Multiply  the  area  of  the  top 
plate,  top  angles  and  bottom  angles,  each  by  the  square  of  the  dis- 
tance of  its  center  of  gravity  from  the  center  of  web;  add  to  these 
results  the  moment  of  inertia  of  the  webs,  which  may  be  taken 
from  the  table  on  page  12,  and  the  moment  of  inertia  of  each  angle 
about  an  axis  through  its  center  of  gravity.  From  the  result  sub- 
tract the  product  of  the  area  of  the  section  by  the  square  of  the 
distance  from  the  neutral  axis  to  the  center  of  the  web,  and  the 
result  will  be  the  required  moment  of  inertia  of  the  section  about 
an  axis  through  the  center  of  gravity  perpendicular  to  the  web. 

The  moment  of  inertia  of  the  top  plate  about  an  axis  through 
its  center  of  gravity  should,  strictly  speaking,  be  added  to  the 
above,  but  its  value  in  the  present  instance  is  so  small  that  the  final 
result  is  not  materially  affected. 

A  somewhat  easier  method,  especially  when  the  operation  has 
to  be  performed  without  the  aid  of  a  slide  rule  is  the  following: 

X  7-I9—329-S2 
X  6.11-157.54 


Top  plate  17  X  %=•  6.38  X  7.19=45.87 
2  top  angles  3  X  3  X  %—  4.22  X  6.11=25.78 

71-65 
2  web  plates        14  X  ^=10.50 

2  bot.  angles  4  X  3  X  ^8=  7.96  X  6.13=48.79 
29.06  X  0.79=22.86 


deduct,  29.06  X  0.792 


171.50 
X  6.13—299.11 


957-97 
+     9.36 


967.33 
-  17-99 


1=949-34 

This  plan  avoids  the  use  of  squares  in  getting  the  moment  of 
inertia  and  saves  cne  multiplication  in  getting  the  position  of  i he 
neutral  axis. 


The  word  eccentricity  is  used  in  the  tables  to  denote  the  dis- 
tance of  the  neutral  axis  of  the  section  from  the  center  of  the  web. 

In  the  calculation  of  these  sections  for  moments  of  inertia 
sideways,  the  distance  out  to  out  of  webs  was  assumed  equal  to  the 
width  of  top  plates,  less  twice  the  nominal  length  of  leg  of  top 
angle. 

The  table  for  two  angles,  page  14,  is  based  on  the  assumption 
that  the  angles  are  attached  to  each  other  securely  enough  to  act  as 
one  member;  if  the  angles  are  not  so  connected,  then  the  least  value 
of  r  a  for  one  angle  should  be  used,  and  the  column  considered  as 
two  separate  members. 

STRENGTH  OF  COLUMNS. 

By  means  of  the  table  of  values  of  —  the  working  strength  of 
any  column  for  which  ri  is  known,  can  be  readily  obtained. 

EXAMPLE:  Required  the  working  strength  of  a  medium  steel 
column  18  feet  long,  square  at  both  ends,  made  up  as  section  81  on 
page  61. 

The  value  of  r"*  is  37.0  and  the  area  38.72  square  inches. 

Referring  to  the  table  of  — ,  look  down  the  column  headed  r% 
until  we  come  to  37.0;  then  in  the  same  horizontal  line,  under  18, 
find  9  for  the  value  of  — ;  referring  now  to  the  tables  of  working 
strength  of  medium  steel  columns  we  find  opposite  9  the  working 
strength  per  square  inch  of  14479  Ibs.  The  total  working  strength 
of  the  column  will  then  be: 

14479  x  38.72  =  560626.82  Ibs. 

BEARING  AND  SHEARING  VAI,UE  OF  RIVETS. 
This  table  is  designed  to  facilitate  the  calculation  of  pitch  and 
diameter  of  rivets  uniting  flanges  and  web  at  the  ends  of  stringers 
and  beams.  Assuming  the  shear  as  acting  in  lines  of  45  degrees 
the  total  stress  is  transferred  from  web  to  flanges  in  a  distance 
equal  to  the  effective  depth  of  the  stringer  or  beam.  If,  therefore, 
we  divide  the  total  stress  by  the  effective  depth  of  beam  we  will 
obtain  the  shear  per  vertical  foot  of  beam  or  its  equivalents,  the 
shear  per  horizontal  running  foot  of  beam.  Dividing  this  shear  per 
foot  run  by  the  allowed  unit  stress  for  bearing  or  shearing  we  ob- 
tain the  required  bearing  or  shearing  area  of  rivets  to  be  provided 
for  each  running  foot,  and  an  inspection  of  the  table  will  show  at 


once  the  necessary  pitch,  size  of  rivet  and  thickness  of  web  required 
to  give  this  area. 

EXAMPLE:  Given  a  stringer  or  beam  with  an  effective  depth  of  3 
feet  and  a  shear  at  the  end  of  45,000  pounds.  What  pitch  and  diam- 
eter of  rivet  will  be  required  to  transmit  the  shear  to  the  flanges 
without  exceeding  a  bearing  pressure  of  12,000  pounds  per  square 
Inch  or  a  shearing  strain  of  8,000  pounds  per  square  inch  on  the 
rivets? 

45,000  Ibs.  -*-  3  =  15,000  Ibs.  per  foot  run. 

•*-  12,000  =  1.25  bearing  area  required. 
•*•    8,000  =  1.88  shearing  area  required. 

Referring  now  to  the  table  we  find  that  for  a  ft"  web  %" 
rivets  would  require  a  pitch  of  3",  giving  a  bearing  area  of  1.31 
square  inches  and  2.41  square  inches  for  single  shear,  or  4.81  for 
double  shear.  With  a  ^"  web  3^"  pitch  would  give  the  same 
bearing  area  and  would  give  2.06  square  inches  for  single  shear  or 
4.12  square  inches  for  double  shear. 

Using  %"  rivets,  a  %"  web  would  require  a  pitch  of  2%"  giving  1.35 
square  inches  for  bearing  and  2.12  square  inches  for  single  and  4.24 
square  inches  for  double  shear.  A  -^"  web  would  permit  3"  pitch 
and  give  i  31  square  inches  for  bearing  and  1.77  square  inches  for 
single  or  3.53  square  inches  for  double  shear. 

RESISTANCE  OF  GIRDER  WEBS  AGAINST  BUCKLING. 

This  table  will  indicate,  when  the  shear  per  foot  run  is  known, 
whether  stiffeners  are  necessary  or  not.  If  stiffeners  are  required 
the  table  will  show  the  proper  clear  distance  between  them.  The 
application  of  the  table  will  be  illustrated  by  the  following; 

EXAMPLE:  Given  a  stringer  or  beam  with  an  effective  depth 
of  3  feet  and  a  shear  at  the  end  of  45,000  pounds.  Will  stiffeners  be 
required,  and  if  so,  how  far  apart  should  they  be  placed? 

The  shear  per  foot  run  equals 

45,000  Ibs.  •+•  3  =  15,000  Ibs. 

Referring  now  to  the  table  and  assuming  that  a  ft"  web  has 
been  adopted  we  find  that  in  the  column  headed  "t  equals  %,"  that 
15,000  falls  between  14,360  and  16,500,  corresponding  to  a  spacing  of 
stiffeners  of  2  feet  6  inches  and  2  feet  3  inches.  This  spacing  being 
less  than  the  clear  vertical  distance  between  horizontal  angles  in- 


dicates  that  stiffeners  are  necessary,  and  indicates,  also,  that  the 
end  stiffeners  should  be  spaced  apart  a  distance  not  exceeding  2  feet 
3  inches. 

Should  this  shear  be  produced  by  a  concentrated  load  on  the 
girder,  then  this  spacing  of  stiffeners  should  be  made  uniform 
from  the  end  of  the  girder  to  the  point  of  application  of  the  load. 
If  this  shear  is  produced  by  a  uniformly  distributed  load  the  total 
shear,  and  consequently  the  shear  per  foot  run,  diminishes  toward 
the  center  of  the  girder  and  consequently  the  stiffeners  may  be 
spaced  farther  apart  until  the  clear  distance  between  them  equals 
the  clear  vertical  distance  between  the  horizontal  angles  of  the  gir- 
der. When  the  table  shows  a  distance  apart  between  stiffeners 
greater  than  the  distance  apart  of  the  flange  angles,  stiffeners  will 
not  be  required  to  prevent  buckling  of  the  webs.  By  referring  to 
the  column  headed  "t  equals  y^"  it  appears  that  if  a  -^  web  is  used 
stiffeners  would  not  be  required,  as  their  distance  apart  would  just 
equal  the  clear  vertical  distance  between  flange  angles.  If  a  T5^ 
web  were  used  stiffeners  would  be  required  i  foot  and  9  inches  apart 
in  the  clear. 

The  several  formulae  in  use  have  for  the  numerator  constants 
varying  from  8,000  to  15,000.  10,000  has  been  adopted  in  the  present 
case,  partly  because  it  will  in  ordinary  cases  give  fair  results  and 
partly  because  in  case  it  is  desired  to  use  another  formula  the  pres- 
ent formula  may  be  readily  adapted  to  another  constant  by  a  ready 
percentage  comparison. 

CENTRIFUGAL  FORCE. 

This  table  shows,  for  various  velocities  and  degrees  of  curva- 
ture, the  amount  of  centrifugal  force,  expressed  in  the  form  of  per 
cent,  of  weight.  It  will  be  found  useful  in  determining  the  stresses 
in  lateral  bracing  due  to  moving  loads  on  bridges  located  on 
curves,  and  its  application  is  as  follows  : 

Obtain  in  the  usual  manner  the  maximum  shearing  stresses  in 
the  various  panels  of  the  truss,  due  to  the  specified  rolling  load,  and 
in  the  same  manner  as  if  the  truss  were  on  a  tangent.  Multiply 
these  shearing  stresses  by  the  tabular  coefficient  corresponding  to 
the  degrees  of  curvature  and  desired  velocity  and  the  results  will  be 
the  shearing  stresses  due  to  the  centrifugal  force. 


STRENGTH  OF  TIMBER  BEAMS. 

The  use  of  the  tables  of  bending  moments  and  capacities  of 
timber  beams  will  be,  perhaps,  best  illustrated  by  the  following  : 

EXAMPLE  :  Required  the  size  of  joist  to  support  a  load  of  100 
Ibs.  per  square  foot,  the  length  of  span  being  18  feet,  the  joists  to  be 
spaced  2  feet  center  to  center  and  the  unit  stress  not  to  exceed  1000 
Ibs.  per  square  inch. 

Assume  the  weight  of  joists  and  flooring  to  be  20  Ibs.  per  square 
foot. 

From  the  table  of  bending  moments  we  find — 

For  20  Ibs.  per  square  foot  and  18  foot  span,  1620  foot  Ibs. 
"  100   "  "      18    "  8100 

Total  bending  moment  =  9720 

Referring  now  to  the  table  of  capacities  for  1000  Ibs.  fiber  strain 
we  find  that  3"  X  16",  3^"  X  15"  or  4"  X  14"  will  answer  the  purpose, 
the  3"  X  16*  being  the  most  economical  in  material. 

For  other  spacing  of  joists  than  24  inches,  obtain  the  load  per 
lineal  foot  of  joist  and  then  select  the  corresponding  bending  mo- 
ments and  proceed  as  above.  If,  in  the  above  example,  the  spacing 
of  joists  was  18  inches  instead  of  24,  the  operation  would  be  as  fol- 
lows : 

20  Ibs.  per  square  foot  X  i  %  =  30  Ibs.  per  lineal  foot, 
And  100  "  X  1^=150    " 

For  30  Ibs.  per  lineal  foot,  and  18  ft.  span  the 

bending  moment       ......         =  1215  ft.  Ibs. 

For  158  Ibs  per  lineal  foot,  and  18  foot  span  the 

bending  moment       ......         =6075      " 

Total  bending  moment  =  7290      " 

This  bending  moment  on  the  basis  of  1000  Ibs.  fiber  strain, 
would  call  for  joists  i%n  X  15",  3"  X  14"  or  4"  X  12",  the  deepest  one 
being  the  stiffest  as  well  as  the  most  economical  in  material. 


MOMENTS  OF  INERTIA. 

§RE 

CTANGLES. 

Depth 
in 
Inches 

•      Width  of  Rectangle  in  Inches 

X 

ft 

3/8 

Tv 

'  y^ 

T9* 

# 

3 

0.56 

0.70 

0.84 

0.98 

1.13 

1.27 

1.41 

4 

1.33 

1.67 

2.00 

2.33 

2.67 

3.00 

3.33 

5 

2.60 

3.26 

3.91 

4-56 

5.21 

5.86 

6.51 

6 

4.50 

5.63 

6.75 

7.88 

9.00 

10.13 

11.25 

7 

7.15 

8.93 

10.72 

12.51 

14.29 

16.08 

17  86 

8 

10.67 

13.33 

16.00 

18.67 

21.33 

24-00 

26,67 

9 

15.19 

18.98 

22.78 

26.58 

30.38 

34.17 

37.97 

10 

20.83 

26.04 

31.25 

36.46 

41.67 

46.87 

52.08 

12 

36.00 

45.00 

54.00 

63.00 

72.00 

81.00 

90.00 

13 

45.77 

57.21 

68.66 

80.10 

91.54 

102.98 

114.43 

14 

57.17 

71.46 

85.75 

100.04 

114.33 

128.63 

142.92 

15 

70.31 

87.89 

105.47 

123.05 

140.63 

158.20 

175.78 

16 

85.33 

106.67 

128.00 

149.33 

170.67 

192.00 

213.33 

17 

102.35 

127.94 

153.53 

179.12 

204.71 

230.30 

255.89 

18 

121.50 

151.88 

182.25 

212.63 

243.00 

273.38 

303.75 

20 

166.67 

208.33 

250.00 

291.67 

333.33 

375.00 

416.67 

21 

192.94 

241.17 

289.41 

337.64 

385.88 

434.11 

482.34 

22 

221.83 

277.29 

332.75 

388.21 

443.67 

499.13 

554.58 

23 

253.48 

316.85 

380.22 

443.59 

506.96 

570.33 

633.70 

24 

288.00 

360.00 

432.00 

504.00 

576.00 

648.00 

720.00 

25 

325.52 

406.90 

488.28 

569.66 

651.04 

732.42 

813.80 

26 

366.17 

457.71 

549.25 

640.79 

732.33 

823.88 

915.42 

27 

410.06 

512.58 

615.09 

717.61 

820.13 

922.64 

1025.16 

28 

457.33 

571.67 

686.00 

800.33 

914.67 

1029.00 

1143.33 

29 

508.10 

635.13 

762.16 

889.18 

1016.21 

1143.23 

1270.26 

30 

562.50 

703.13 

843.75 

984.38 

1125.00 

1265.63 

1406.25 

32 

682.67 

853.33 

1024.00 

1194.67 

1365.33 

1536.00 

1706.67 

34 

818.83 

1023.54 

1228.25 

1432.96 

1637.67 

1842.38 

2047.08 

36 

972.00 

1215.00 

1458.00 

1701.00 

1944.00 

2187.00 

2430.00 

38 

1143.17 

1428.96 

1714.75 

2000.54 

2286.33 

2572.13 

2857.92  . 

40 

1333.33 

1666.67 

2000.00 

2333.33 

2666.67 

3000.00 

3333.33 

44 

1774.67 

2218.33 

2662.00 

3105.67 

3549.33 

3993.00 

4436.67 

46 

2027.83 

2534.79 

3041.75 

3548.71 

4055.67 

4562.63 

5069.58 

48 

2304.00 

2880.00 

3456.00 

4032.00 

4608.00 

5184.00 

5760.00 

50 

2604.17 

3255.21 

3906.25 

4557.29 

5208.33 

5859.38 

6510.42 

60 

4500.00 

5625.00 

6750.00 

7875.00  9000.00 

10125.00 

11250.00 

MOMENTS  OF  INERTIA.—  RECTANGLES. 

(CONTINUED.) 

Width  of  Rectangle  in  Inches 

Depth 
in 

Inches 

u 

X 

11 

H 

it 

1 

1.55 

1.69 

1.83 

1.97 

2.11 

2.25 

3 

3.67 

4.00 

4.33 

4.67 

5.00 

5.33 

4 

7.16 

7.81 

8.46 

9.11 

9.77 

10.42 

5 

12.38 

13.50 

14.63 

15.75 

16.88 

18.00 

6 

19.65 

21.44 

23.22 

25.01 

26.80 

28.58 

7 

29.33 

32.00 

34.67 

37.33 

40.00 

42.67 

8 

41.77 

45.56 

49.36 

53.16 

56.95 

60.75 

9 

57.29 

62.50 

67.71 

72.92 

78.13 

83.33 

10 

99.00 

108.00 

117.00 

126.00 

135.00 

144.00 

12 

125.87 

137.31 

148.75 

160.20 

171.64 

183.08 

13 

157.21 

171.50 

185.79 

200.08 

214.38 

228.67 

14 

193.36 

210.94 

228.52 

246.09 

263.67 

281.25 

15 

234.67 

256.00 

277.33 

298.67 

320.00 

341.33 

16 

281.47 

307.06 

332.65 

358.24 

383.83 

409.42 

17 

334.13 

364.50 

394.88 

425.25 

455.63 

486.00 

18 

458.33 

500.00 

541.67 

583.33 

625.00 

666.67 

20 

530.58 

578.81 

627.05 

675.28 

723.52 

77J..75 

21 

-  610.04 

665.50 

720.96 

776.42 

831.87 

887.33 

22 

697.07 

760.44 

823.81 

887.18 

950.55 

1013.92 

23 

792.00 

864.00 

936.00 

1008.00 

1080.00 

1152.00 

24 

895.18 

976.56 

1057.94 

1139.32 

1220.70 

1302.08 

25 

1006.96 

1098.50 

1190.04 

1281.58 

1373.13 

1464.67 

26 

1127.67 

1230.19 

1332.70 

1435.22 

1537.73 

1640.25 

27 

1257.67 

1372.00 

1486.33 

1600.67 

1715.00 

1829.33 

28 

1397.29 

1524-31 

1651.34 

1778.36 

1905.39 

2032.42 

29 

1546.88 

1687.50 

1828.13 

1968.75 

2109.38 

2250.00 

30 

1877.33 

2048.00 

2218.67 

2389.33 

2560.00 

2730.67 

32 

2251.79 

2456.50 

2661.21 

2865.92 

3070.63 

3275.33 

34 

2673.00 

2916.00 

3159.00 

3402.00 

3645.00 

3888.00 

36 

3143.71 

3429.50 

3715.29 

4001.08 

4286.88 

4572.67 

38 

3666.67 

4000.00 

4333.33 

4666.67 

5000.00 

5333.33 

40 

4880.33 

5324.00 

5767.67 

6211.33 

6655.00 

7098.67 

44 

5576.54 

6083.50 

6590.46 

7097.42 

7604.38 

8111.33 

46 

6336.00 

6912.00 

7488.00 

8064.00 

8640.00 

9216.00 

48 

7161.46 

7812.50 

8463.54 

9114.58 

9765.63 

10416.67 

50 

,  12375.00 

13500.00 

14625.00 

15750.00 

16875.00 

18000.00 

60 

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ONE  PLATE 


TWO  ANGLES. 


1 


k 

One  Plate, 
Size  in 
Inches 

TWO  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A  B 

Eccen- 
tricity 

Axis 
C  D 

r2 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

i 

6XX 

2^X2 

X 

3.62 

10.6 

2.93 

1.44 

0.86 

2 

ft 

4.12 

11.1 

2.69 

1.55 

0.95 

3 

3      X2J£ 

X 

4.12 

11.2 

2.72 

1.49 

1.26 

4 

3^X2^ 

ft 

5.06 

12.3 

2.43 

1.66 

2.00 

5 

6X# 

2^X2 

1A 

4.37 

14.1 

3.23 

1.19 

0.78 

6 

A 

4.87 

14.9 

3.06 

1.31 

0.86 

7 

3      X2y2 

X 

4.87 

14.9 

3.06 

1.26 

1.13 

8 

3^X2^ 

A 

5.81 

16.2 

2.79 

1.45 

1.84 

9 

7XX 

2^X2 

1A 

3.87 

16.3 

4.21 

l.£2 

0.80 

10 

T\ 

4.37 

17.2 

3.94 

1.76 

0.89 

11 

3vy  o  »  / 
/Z 

\/ 

4.37 

17.1 

3.91 

1.70 

1.19 

12 

3i/2X2i/2 

A 

5.31 

18.6 

3.50 

1.92 

1.90 

13 

7X# 

2^X2 

X 

4.75 

21.8 

4.59 

1.32 

0.72 

14 

A 

5.25 

22.9 

4.36 

1.47 

0.80 

15 

3      X2# 

2 

5.25 

22.8 

4.34 

1.42 

1.05 

16 

3>£X2i^ 

6.19 

25.1 

4.05 

1.64 

1.73 

17 

8XX 

2^X2 

A 

4.62 

25.0 

5.41 

1.95 

0.84 

18 

3      X2j£ 

4.62 

24.9 

5.39 

1.89 

1.13 

19 

3^X2^ 

A 

5.56 

27.0 

4.86 

2.15 

1.82 

20 

4      X3 

H 

6.96 

29.4 

4.22 

2.29 

2.56 

21 

8X^ 

2%X2 

ft 

5.62 

33.5 

5.96 

1.60 

0.75 

22 

3      X2  ^ 

X 

5.62 

33.0 

5.87 

1.56 

0.98 

23 

A 

6.56 

36.3 

5.53 

1.82 

1.63 

24 

4  2X3  2 

H 

7.96 

39.1 

4.91 

2.01 

•2.35 

25 

9XX 

3      X2^ 

X 

4.87 

34.4 

7.06 

2.07 

1.07 

26 

3>£X2^ 

A 

5.81 

37.7 

6.49 

2.36 

1.74 

27 

4      X3 

3^ 

7.21 

40.4 

5.60 

2.56 

2.47 

28 

TV 

7.99 

41.6 

5.21 

2.66 

2.60 

ONE  PLATE.     TWO  ANGLES. 

(CONTINUED.) 


SO. 

One  Plate, 
Size  in 
Inches 

TWO  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A  B 

Eccen- 
tricity 

Axis 
CD 
r2 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

29 

9X^ 

3      X2% 

1A 

6.00 

46.0 

7.67 

1.68 

0.92 

30 

3^X2^ 

T\ 

6.94 

50.5 

7.28 

1.98 

1.54 

31 

4      X3 

y% 

8.34 

54.5 

6.53 

2.21 

2.24 

32 

7 

9.12 

56.2 

6.16 

2.33 

2.39 

33 

lOXi^ 

3      X2y2 

X 

5.12 

46.4 

9.06 

2.22 

1.02 

34 

3^X2^ 

(L 

6.06 

50.7 

8.37 

2.56 

1.67 

35 

4      X3 

y% 

7.46 

54.1 

7.25 

2.81 

2.38 

36 

A 

8.24 

57.6 

6.99 

2.93 

2.52 

37 

lOX^ 

3      X2y2 

l/i 

6.37 

61.7 

9.69 

1.79 

0.88 

38 

3  1^X2  yz 

7.31 

68.0 

9.30 

2.12 

1.46 

39 

4      X3 

y% 

8.71 

73.3 

8.42 

2.40 

2.15 

40 

A 

9.49 

75.7 

7.98 

2.54 

2.30 

41 

12X^ 

3%X2% 

5^ 

6  56 

84.6 

12.90 

2.91 

1.54 

42 

4      X3 

y% 

7.96 

90.9 

11.42 

3.25 

2.24 

43 

5      X3 

y% 

8.72 

95.2 

10.92 

3.48 

3.89 

44 

5      X3^ 

y* 

9.10 

95.2 

10.46 

3.45 

3.75 

45 

12X^ 

3^X2^ 

fV 

8.06 

112.9 

14.01 

2.37 

1.33 

46 

4      X3  2 

^ 

9.46 

122.0 

12.90 

2.74 

1.98 

47 

5      X3 

H 

10.22 

128.6 

12.58 

2.97 

3.44 

48 

5      X3% 

14 

10.60 

128.7 

12.14 

2.96 

3.34 

49 

14XT5.I 

3^X2^ 

A 

7.94 

152.9 

19.26 

2.85 

1.31 

50 

4      X3 

^ 

9.34 

165.5 

17.72 

3.30 

1.95 

51 

5      X3 

y% 

10.10 

173.9 

17.22 

3.57 

3.43 

52 

5      X3^ 

y* 

10.48 

173.9 

16.59 

3.57 

3.31 

53 

14X^ 

3^X2^ 

A 

8.81 

173.4 

19.68 

2.57 

1.21 

54 

4      X3 

^8 

10.21 

188.4 

18.45 

3.02 

1.83 

55 

5      X3 

Ks 

10.97 

198.5 

18.10 

3.28 

3.21 

56 

5     X3% 

Ks 

11.35 

198.5 

17.49 

3.30 

3.12 

ONE  PLATE. 


T 


TWO  ANGLES. 


No. 

One  Plate, 
Size  in 
Inches 

TWO  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A  B 

Eccen- 
tricity 

Axis 
CD 
r2 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

57 

15xT5s 

3X3 

A 

8.25 

179.9 

21.81 

2.86 

0.82 

58 

4X3 

•A 

9.65 

200.9 

20.82 

3.45 

1.89 

59 

5X3 

y% 

10.41 

210.8 

20.25 

3.74 

3.32 

60 

5X3^ 

H 

10.79 

211.4 

19.59 

3.75 

3.22 

61 

15X^ 

3X3 

A 

9.19 

204.3 

22.23 

2.57 

0.77 

62 

4X3 

3A 

10.59 

228.2 

21.55 

3.15 

1.77 

63 

5X3 

y& 

11.35 

240.5 

21.19 

3.43 

3.10 

64 

5X3^ 

3A 

11.73 

241.1 

20.55 

3.45 

3.02 

65 

16xfV 

4X3 

3A 

9.96 

240.0 

24.10 

3.60 

1.83 

66 

5X3 

y% 

10.72 

253.4 

23.64 

3.89 

3.23 

67 

5X3^ 

12.06 

262.1 

21.74 

4.17 

3.36 

68 

6X4 

2 

13.36 

272.4 

20.39 

4.41 

5.13 

69 

IQX3/S 

4X3 

3A 

10.96 

273.2 

24.93 

3.27 

1.71 

70 

5X3 

H 

11.72 

288.4 

24.61 

3.56 

3.00 

71 

5X3^ 

13.06 

299.6 

22.94 

3.85 

3.16 

72 

6X4 

T76 

14.36 

312.1 

21.74 

4.10 

4.85 

73 

16X# 

4X3 

3A 

12.96 

334.4 

25.80 

2.76 

1.52 

74 

5X3 

3A 

13.72 

352.8 

25.72 

3.04 

2.67 

75 

5X3^ 

y* 

16.00 

379.3 

23.71 

3.55 

3.08 

76 

6X4 

n 

17.50 

396.0 

22.63 

3.81 

4.72 

77 

16X^ 

4X3 

JLJ 

16.50 

421.2 

25.53 

2.82 

1.69 

78 

5X3 

y* 

17.50 

443.4 

25.34 

3.11 

2.86 

79 

5X3^ 

X 

19.84 

469.0 

23.64 

3.50 

3.24 

80 

6X4 

21.72 

490.7 

22.59 

3.76 

4.91 

81 

18X  5 

4X3 

N 

10.59 

333.9 

31.53 

3.85 

1.73 

82 

5X3 

H 

11.35 

351.7 

30.99 

4.18 

3.05 

83 

5X3  % 

12.69 

365.3 

28.79 

4.52 

3.19 

84 

6X4 

1 

13.99 

381.2 

27.25 

4.80 

4.90 

ONE  PLATE.     TWO  ANGLES. 

(CONTINUED.) 


No. 

One  Plate, 
Size  in 
Inches 

TWO  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A  B 

Eccen- 
tricity 

Axis 
CD 
r2 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

85 

18X^ 

4      X3 

# 

11.77 

379.4 

32.40 

3.48 

1.60 

86 

5     X3 

H 

12.47 

399.4 

32.03 

3.81 

2.83 

87 

5     X3% 

A 

13.81 

417.2 

30.21 

4.15 

2.99 

88 

6      X4 

15.11 

434.7 

28.77 

4.45 

3.48 

89 

18X^ 

4      X3 

% 

15.50 

499.2 

32.21 

3.43 

1.71 

90 

5      X3 

y* 

16.50 

526.7 

31.92 

3.75 

2.98 

91 

5      X3^ 

% 

17.00 

527.9 

31.05 

3.81 

2.91 

92 

6      X4 

X 

18.50 

552.5 

29.87 

4.11 

4.47 

93 

18X# 

4      X3 

H 

19.21 

617.5 

32.15 

3.37 

1.82 

94 

5     X3 

fa 

20.47 

651.2 

'31.81 

3.69 

3.14 

95 

5      X3% 

ft 

21.09 

652.8 

30.95 

3.76 

3.04 

96 

6     X4 

22.97 

682.7 

29.72 

4.07 

4.65 

97 

2Qxy& 

3y2X3y2 

H 

12.46 

496.9 

39.88 

3.58 

1.04 

98 

5     X3}£ 

y* 

13-60 

537.4 

39.51 

4.10 

2.60 

99 

6      X4 

14.72 

562.2 

38.19 

4.44 

4.06 

100 

20Xi^ 

3y2X3y2 

J/2 

16.50 

655.6 

39.73 

3.52 

1.13 

101 

o      X  3  ^2 

y> 

18.00 

708.6 

39.37 

4.04 

2.74 

102 

6      X4 

y* 

19.50 

741.4 

38.02 

4.39 

4.24 

103 

8      X6 

23.52 

795.9 

33.84 

4.90 

8.04 

104 

20Xj^ 

3y2X3i/2 

y& 

20.46 

810.8 

39.63 

3.46 

1.22 

105 

5      X3y2 

* 

22.34 

876.5 

39.23 

3.99 

2.87 

106 

6     X4 

24.22 

918.4 

37.92 

4.34 

4.41 

107 

8     X6 

H 

29.38 

984.4 

33.51 

4.87 

8.37 

108 

20X^ 

3y2X3y2 

X 

24.38 

961.1 

39.42 

3.41 

1.34 

109 

5      X3  V2 

X 

26.62 

1041.0 

39.11 

3.93 

3.05 

110 

6      X4 

28.88 

1090.0 

37.75 

4.29 

4.63 

111 

8      X6 

X 

34.88 

1168.0 

33.49 

4.79 

8.71 

c 

•ssssss 

mamcm 

TWO 

PLATES 

Ar--J|l 

--B 

TWO 

ANG 

LES 

1 

D 

Web  Plate 

Top  Plate 

TWO  ANGLES 

Total 

AXIS  ] 

LB 

Axis 

No. 

Size  in 
Inches 

Size  in 
Inches 

Size  in  Inches 

Area 
Square 

i  l  t 

I 

r2 

Eccen- 
tricity 

CD 

r2 

Inches 

1 

6X# 

?x* 

3X2#XX 

5.87 

14.8 

2.52 

1.98 

2.J9 

2 

H 

y& 

7.97 

16.5 

2.06 

2.16 

2.34 

3 

l/2 

10.00 

18.3 

1.83 

2.26 

2.48 

4 

6X^g 

8X^  • 

3X2%X% 

7.87 

22.1 

2.81 

2.00 

2.80 

5 

y* 

H 

10.09 

24.2 

2.44 

2.16 

2.95 

6 

* 

12.25 

26.5 

2.17 

2.27 

3.10 

7 

7X^ 

7X% 

3X3      XT«ff 

7.06 

22.9 

3.24 

2.23 

1.95 

8 

H 

y?> 

8.60 

25.3 

2.94 

2.41 

2.17 

9 

y* 

10.75 

27.8 

2.59 

2.54 

2.32 

10 

7Xf£ 

BXJf 

3X3     XT\ 

9.19 

33.9 

3.69 

2.22 

2.51 

11 

/£ 

n 

10.85 

36.8 

3.39 

2.40 

2.75 

12 

K 

% 

13.13 

40.2 

3.06 

2.53 

2.90 

13 

8X14: 

8Xi^ 

3X3      X^ 

7.56 

32.8 

4.34 

2.57 

2.28 

14 

H 

^i 

9.22 

35.0 

3.90 

2.79 

2.59 

15 

y*> 

11.50 

39.3 

3.42 

2.95 

2.78 

16 

8X3^ 

9X^ 

3X3      XT\ 

9.94 

48.7 

4.90 

2.55 

3.00 

17 

l/2 

f^ 

11.72 

53.1 

4.53 

2.75 

3.32 

18 

M 

14.13 

57.3 

4.06 

2.91 

3.49 

19 

9XT5? 

9X^ 

4X3      X^ 

11.15 

60  0 

5.38 

3.08 

3.68 

20 

% 

% 

13.81 

65.3 

4.73 

3.27 

3.98 

21 

H 

ft 

16.40 

69.3 

4.23 

3.41 

4.19 

22 

9X^ 

lOXSXi 

4X3      X^ 

12  09 

70.5 

5.83 

2.98 

.13 

23 

I/ 

i£ 

14.88 

75.7 

5.09 

3.20 

.49 

24 

H 

H 

17.59 

80.8 

4.59 

3.35 

.75 

25 

10XT55 

lOX^j 

4X3      X^g 

11.84 

81.6 

6.89 

3.41 

.18 

26 

\/ 

r/ 

14.63 

86.9 

5.94 

3.65 

.53 

27 

H 

^ 

17.34 

92.1 

5.31 

3.81 

.78 

28 

iox^£ 

12X^g 

4X3      X^£ 

13.21 

96.4 

7.30 

3.35 

5.50 

29 

y* 

^ 

16.25 

102.8 

6.33 

3.61 

5.98 

30 

H 

19.21 

109.9 

5.72 

3.78 

6.32 

31 

10X^ 

12XJ£ 

4X3      X^g 

15.96 

127.6 

8.00 

3.28 

5.74 

33 

H 

% 

19.00 

135.8 

7.15 

3.52 

6.13 

33 

32 

% 

21.96 

143.4 

6.53 

3.70 

6.42 

24 


TWO  PLATES.     TWO  ANGLES. 

(CONTINUED.) 

No. 

Web  Plate 
Size  in 
Inches 

Top  Plate 
Size  in 
Inches 

TWO  ANGLES 

Total 
Area 
Square 
Inches 

AXIS  A  B 

Eccen- 
tricity 

.17 

Axis 
CD 
r2 

Size  in  Inches 

I 

r2 

34 

12X-5 

i2x  y% 

5X3     x^ 

13.97 

139.2 

9.97 

6.31 

35 
36 

N 

X 

X 

ft 

17.25 
20.47 

148.3 
156.8 

8.59 
7.66 

.46 
.65 

6.86 
7.24 

37 

12X^ 

i4x  y% 

5X3^X^ 

15.85 

165.3 

10.43 

.03 

7.64 

38 
39 
40 

I 

% 

ft 

19.50 
23.09 
26.62 

177.3 

187.4 
195.5 

9.09 
8.12 
7.34 

.33 
.54 
.70 

8.29 
8.76 
9.13 

41 

12X>£ 

14X1 

5X3i^X^g 

26.10 

257.9 

9.88 

4.69 

10.17 

42 
43 

2  2 

X 

ft 

35.00 
43.84 

298.3 
339.1 

8.52 
7.74 

5.21 
5.60 

11.21 
11.84 

44 

14XJ/6 

i4x  y% 

6X3^X^ 

17.34 

255.9 

14.76 

4.63 

8.39 

45 
46 
47 

n 

ft 

y* 

ft 

21.25 
25.10 
28.87 

273.7 
287.7 
299  0 

12.88 
11.46 
10.36 

5.00 
5.25 
5.44 

9-13 
9.68 
10,11 

48 

14X^ 

14X1 

6x3^x^6 

27.84 

391.5 

14.06 

5.30 

10.43 

49 

lj£ 

yt 

37.00 

442.7 

11.96 

5.90 

11.49 

50 

2 

ft 

46.10 

494.5 

10.73 

6.33 

12.16 

51 

16X^ 

i4x  yz 

6X4      Xy£ 

18.47 

371.3 

20.11 

5.09 

7.88 

52 

y* 

y* 

22.50 

395.9 

17.60 

5.53 

8.64 

53 

54 

9 

y* 

26.47 
30.38 

417.1 
428.8 

15.76 
14.12 

5.83 
6.07 

9.18 
9.62 

55 

16Xi^ 

i 

6X4      xy^ 

29.22 

563.2 

19.28 

5.82 

9.94 

56 

1K 

y* 

38.50 

634.1 

16.50 

6.50 

11.05 

57 

2 

ft 

47.72 

700.9 

14.69 

6.99 

11.75 

58 

18X^ 

i4x  y% 

6X4      X^ 

19.22 

514.7 

26.78 

5.54 

7.57 

59 

% 

K 

23.25 

550.9 

23.70 

6.06 

8.36 

60 
61 

ft 
X 

# 

M 

27.22 
31.13 

575.3 
601.4 

21.15 
19.30 

6.43 
6.69 

8.92 
9.38 

62 

18XJ£ 

14X1 

6X4      X^j 

30.22 

775.7 

25.67 

6.33 

9.61 

63 

64 

2  2 

% 

39.50 
48.72 

868.6 
952.9 

21.99 
19.56 

7.11 
7.66 

10.77 
11.51 

65 

18X^6 

14X1 

6X4      X^£ 

32.47 

920.8 

28.36 

5.89 

9.01 

66 

67 

2 

y* 

ft 

41.75 
50.97 

985.2 
1134.1 

23.60 
22.25 

6.73 
7.33 

10.26 
11.07 

c 

n  :  ir 

THREE  PLATES.    A--1-  ---•  j-~  M--B     TWO  ANGLES. 

1  i  1 

No. 

Two  Web 
Plates, 
Size  in 
Inches 

Top 
Plate, 
Size  in 
Inches 

TWO  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

Eccen- 
tricity 

Axis 
C.D. 
r2 

Dis- 
tance 
Betw'n 
Webs 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

1 

9XX 

12XX 

2^X2^ 

T\ 

10.44 

78.3 

7.50 

2.39 

12.3 

6.0" 

2 

12xtV 

11.19 

82.3 

7.36 

2.55 

12.3 

3 

9XyV 

12.32 

96.5 

7.84 

2.31 

12.3 

4 

12X/8 

H 

13.59 

102.0 

7.51 

2.51 

12.5 

5 

9X3/£ 

14.71 

116.1 

7.89 

2.31 

12.5 

6 

12XT5 

A 

16.00 

121.8 

7.61 

2.48 

12.7 

7 

9xiV 

17.13 

135.9 

7.94 

2.32 

12.7 

8 

12x^2 

i^ 

18.38 

141.7 

7.71 

2.45 

12.9 

9 

9XK 

19.50 

155.7 

7.98 

2.31 

13.0 

10 

10XX 

12XV 

2^X2^ 

tV 

10.94 

104.4 

9.54 

2.55 

12.2 

11 

12X-5- 

11.69 

109.6 

9.38 

2.73 

12.2 

12 

lOX^, 

12.94 

128.4 

9.92 

2.46 

12.2 

13 

12X>/8 

ZA 

14.21 

135.7 

9.55 

2.68 

12.4 

14 

loxs/g' 

15.46 

154.3 

9.98 

2.46 

12.4 

15 

12X-7-T- 

JL 

16.75 

162.0 

9.68 

2.64 

12.6 

16 

10  XT^ 

18.00 

180.5 

10.0 

2.46 

12.6 

17 

12X^ 

1^ 

19.25 

188.2 

9.78 

2.62 

12.8 

18 

10X^ 

20.50 

206.6 

10.1 

2.46 

12.9 

19 

10  X^ 

14X* 

3     X3 

tV 

12.06 

109.0 

9.04 

2.71 

16.7 

7.0" 

20 

12.94 

114.4 

8.84 

2.88 

16.7 

21 

10XT\ 

14.19 

134.3 

9.47 

2.63 

16.6 

22 

14X3^ 

N 

15.72 

141.8 

9.02 

2.84 

16.9 

23 

ioxa^ 

16.97 

161.6 

9.52 

2.63 

16.9 

24 

14X  -7- 

J7T 
1 

18.49 

169.3 

9.16 

2.81 

17.2 

25 

10XT76 

• 

19.74 

189.0 

9.57 

2.63 

17.2 

26 

14X^ 

I/ 

21.25 

197.0 

9.27 

2.78 

17.4 

27 

10X1^ 

22.50 

216.5 

9.62 

2.63 

17.5 

28 

14X|^ 

H 

25.47 

232.3 

9.12 

2.89 

17.9 

29 

12XX 

15XX 

3      X3 

T5G 

13.31 

181.7 

13.7 

3.10 

20.3 

8.0" 

30 

14.25 

190.7 

13.4 

3.31 

20.1 

31 

12XT\ 

15.75 

223.4 

14.2 

2.99 

20.1 

32 

15X^ 

3/8 

17.35 

236.0 

13.6 

3.25 

20.3 

THREE  PLATES.        TWO  ANGLES. 

(CONTINUED.) 

No. 

ho  \Veb 
Plates, 
Size  in 
Inches 

Top 
Plate, 
Size  in 
Inches 

TWO  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

Eccen- 
tricity 

Axis 
C.  D. 
r2 

Dis- 
tance 
Betw'n 
Webs 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

33 

12X3/8 

15X3/6 

3      X3 

y% 

18.85 

268.6 

14.3 

2.99 

20.4 

8.0" 

34 

L5Xy'7-r 

rV 

20.42 

281.4 

13.8 

3.21 

20.6 

35 

12XT% 

TV 

21.92 

313.8 

14.3 

2.99 

20.7 

36 

15X1^ 

X 

23.50 

327.1 

13.9 

3.18 

20.9 

37 

12X^ 

25.00 

359.4 

14.4 

2.99 

21.0 

38 

15X|^ 

y* 

28.10 

385.2 

13.7 

3.31 

21.4 

39 

14Xi\ 

16XT5r 

3      X3 

P 

17.31 

344.1 

19.9 

3.33 

23.9 

9.0" 

40 

16X3/8 

18.97 

363.7 

19.2 

3.63 

24.2 

41 

14x^/8 

20.72 

413.4 

20.0 

3.33 

24.3 

42 

16X-X 

TV 

22.36 

433.5 

19.4 

3.58 

24.5 

43 

14X-C 

24.11 

482.9 

20.0 

3.32 

24.6 

44 

16X^ 

y2 

25.75 

503.5 

19.6 

3.55 

24.8 

45 

14X^ 

27.50 

552.7 

20.1 

3.32 

24.9 

46 

16XJ^ 

y% 

30.72 

592.6 

19.3 

3.70 

25.2 

47 

14X^6 

34.22 

692.7 

20.2 

3.32 

23.8 

8.5'' 

48 

15X^ 

18XT\ 

3      X3 

T\ 

18.57 

425.6 

22.9 

3.59 

31.0 

10.5" 

49 

18Xf| 

y& 

20.35 

449.9 

22.1 

3.92 

31.2 

50 

15X3/8 

22.22 

511.4 

23.0 

3.59 

31.4 

51 

l8XlV 

TV 

23.99 

536.2 

22.4 

3.87 

31.6 

52 

15X-7^ 

25.87 

597.3 

23.1 

3.59 

31.7 

53 

18X^ 

/^ 

27.63 

622.8 

22.5 

3.83 

31.9 

54 

15X^ 

29.50 

683.8 

23.2 

3.59 

32.1 

55 

18X5^ 

$ 

32.97 

733.1 

22.2 

4.00 

32.4 

56 

15X|^ 

36.72 

857.2 

23.3 

3  59 

32.8 

57 

16XTG 

20XT\ 

3/^x3K 

r, 
TS 

20.43 

524.0 

25.6 

3.93 

37.7 

11.5" 

58 

20X3/8 

y* 

22.46 

553.3 

24.6 

4.28 

38.0 

59 

16X3^ 

24.46 

629.6 

25.7 

3.93 

38.1 

60 

20Xy7^ 

JL 

26.49 

659.4 

24.9 

4.22 

38.4 

61 

16XTT£ 

28.49 

735.2 

25.8 

3.93 

38.5 

62 

20X^ 

X 

30.50 

765.9 

25.1 

4.18 

38.7 

63 

16X^ 

32.50 

841.5 

25.9 

3.92 

38.9 

64 

20X^3 

M 

36.46 

901.2 

24.7 

4.36 

39.3 

65 

16X^ 

40.46 

1055. 

26.1 

3.93 

39.7 

66 

18X3/6 

24X3/8 

4      X4 

H 

28.22 

909.1 

32.1 

4.52 

55.0 

14.0" 

67 

24XF6 

A 

30.62 

951.7 

31.1 

4.86 

55.3 

68 

18X^ 

32.87 

1062. 

32.3 

4.52 

55.5 

69 

24X^ 

K 

35.25 

1106. 

31.4 

4.81 

55.8 

70 

18X  i/^ 

37.50 

1215. 

32.4 

4.53 

56.0 

71 

24X|£ 

^ 

42.22 

1300. 

30.8 

5.01 

56.4 

72^18X5^ 

46.72 

1523. 

32.6 

4.53 

56.9 

73  ' 

24  XV 

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51.38 

1611. 

31.4 

4.92 

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FOUR  ANGLES 

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AXIS  A.  B. 

AXIS  C.  D. 

No. 

Plate, 
Size  in 
Inches 

Size  in 
Inches 

Thick- 
ness 

Area, 
Square 
Inches 

I 

r2 

I 

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1 

6X# 

2^X2 

y* 

5.74 

31.6 

5.51 

6.2 

1.07 

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7.70 

42.9 

5.57 

9.3 

1.21 

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6.74 

36.2 

5.37 

10.3 

1.53 

4 

9.18 

48.9 

5.33 

15.7 

1.71 

5 

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7.26 

40.5 

5.58 

16.0 

2.21 

6 

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9.94 

55.1 

5.54 

24.2 

2.43 

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12.50 

68.1 

5.45 

32.3 

2.59 

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5.34 

10.1 

1.19 

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51.2 

5.15 

16.8 

1.69 

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10.69 

57.4 

5.37 

25.6 

2.40 

11 

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13.25 

70.4 

5.31 

34.2 

2.58 

12 

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5.99 

45.8 

7.64 

6.2 

1.03 

13 

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7.95 

62.1 

7.81 

9.3 

1.17 

14 

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6.99 

52.4 

7.50 

10.3 

1.47 

15 

y% 

9.43 

71.1 

7.53 

15.7 

1.67 

16 

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7.51 

58.4 

7.77 

16.0 

2.13 

17 

3/8 

10.19 

79.6 

7.81 

24.2 

2.37 

18 

12.75 

98.8 

7.75 

32.8 

2.54 

19 

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9.47 

69.4 

7.32 

20.1 

2.13 

20 

y% 

10.95 

80.2 

7.32 

24.2 

2.21 

21 

y 

13.75 

98.8 

7.18 

32.8 

2.38 

22 

4      X3 

J>_, 

10.11 

76.5 

7.57 

29.6 

2.93 

23 

y% 

11.67 

88.2 

7.56 

35.4 

3.03 

24 

yz 

14.75 

109.5 

7.42 

47.8 

3.24 

25 

5      X3 

J>^ 

11.35 

90.5 

7.97 

56.3 

4.96 

26 

$/ 

13.19 

105.0 

7.96 

67.6 

5.12 

27 

% 

16.75 

130.9 

7.81 

90.6 

5.41 

28 

7X^/3 

2^X2 

*A 

8.83 

65.7 

7.44 

10.1 

1.15 

29 

3      X2% 

*/* 

10.31 

74.6 

7.24 

16.8 

1.63 

30 

3  y,  x  2  y 

H 

11.07 

83.2 

7.52 

25.6 

2.32 

31 

13.63 

102.4 

7.51 

34.2 

2.51 

FOUR  ANGLES.     ONE  PLATE. 

(CONTINUED.) 

Ik 

One  Web 
Plate, 
Size  in 
Inches 

FOUR  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  t.  1). 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

I 

r2 

32 

7X^ 

3^X3 

H 

11.83 

83.7 

7.08 

25.7 

2.17 

33 

14.63 

102.4 

7.00 

34.7 

2.37 

34 

H 

17.31 

119.6 

6.91 

43.5 

2.51 

35 

4      X3 

y% 

12.55 

91.8 

7.32 

37.3 

2.97 

36 

y* 

15.63 

113.1 

7.24 

50.1 

3.21 

37 

$ 

18.55 

132.4 

7.14 

62.8 

3.39 

38 

5      X3 

y* 

14.07 

108.6 

7.72 

70.2 

4.99 

39 

17.63 

134.5 

7.63 

94.2 

5.34 

40 

s/i 

21.07 

157.4 

7.47 

118.4 

5.62 

41 

7x/4 

3UX2U 

i/ 

14.50 

106.0 

7.31 

36.1 

2.49 

42 

3y2x3  2 

l/2 

15.50 

106.9 

6.90 

36.7 

2.37 

43 

/& 

18.18 

123.1 

6.77 

46.2 

2.54 

44 

4      X3 

l/2 

16.50 

116.7 

7.07 

52.8 

3.20 

45 

19.42 

135.9 

7.00 

65.9 

3.40 

46 

5     X3 

I/ 

18.50 

138.0 

7.46 

97.9 

5.29 

47 

>6 

21.94 

161.0 

7.34 

123.0 

5.61 

48 

8X.X 

2i4X2 

% 

6.24 

62.9 

10.1 

6.2 

0.99 

49 

a/ 

8.20 

85.3 

10.4 

9.3 

1.12 

50 

3      X2^ 

\£ 

7.24 

72.1 

9.96 

10.3 

1.42 

51 

y% 

9.68 

97.9 

10.1 

15.7 

1.62 

52 

3  l£X2  l£ 

7.76 

80.0 

10.3 

16.0 

2.06 

53 

y 

10.44 

109.2 

10.5 

24.2 

2.32 

54 

y 

13-00 

135.9 

10.5 

32.3 

2.49 

55 
56 

3^X3 

ii 

9.72 
11.20 

95.6 
110.5 

9.83 
9.87 

20.1 
24.2 

2.07 
2.16 

57 

^2 

14.00 

136.8 

9.77 

32.8 

2.34 

58 

4      X3 

A 

10.36 

105.1 

10.1 

29.6 

2.86 

59 

H 

11.92 

121.2 

10.2 

35.4 

2.97 

60 

# 

15.00 

151.0 

10.1 

47.8 

3.18 

61 

5     X3 

11.60 

123.5 

10.6 

56.3 

4.86 

62 

y% 

13.44 

143.4 

10.7 

67.6 

5.03 

63 

i/ 

17.00 

179.4 

10.6 

90.6 

5.33 

64 

5      XZft 

ZA 

14.20 

143.7 

10.1 

67.9 

4.78 

65 

i/ 

18.00 

179.6 

9.98 

91.0 

5.06 

66 

/'Z 

H 

15.68 

164.9 

10.5 

115.6 

7.37 

67 

>/2 

20.00 

208.6 

10.4 

153.9 

7.69 

68 

sx^/g" 

2^X2 

y& 

9.20 

90.6 

9.85 

10.1 

1.10 

69 

3      X2% 

y 

10.68 

103.3 

9.67 

16.8 

1.57 

70 

3}4X2}4 

H 

11.44 

114.6 

10.0 

25.6 

2.24 

71 

14.00 

141.2 

10  1 

34.2 

2.45 

33 


L  A  J 

FOUR   ANGLES,     c  pS"1-*—  '  SB  D    ONE  PLATE. 

1           B          I 

One  Web 

FOUR  ANGLES 

Total 

AXIS  A.  B. 

AXIS  0.  D. 

Plate, 

Area, 

No. 

Size  in 
Inches 

Size  in 
Inches 

Thick- 
ness 

Square 
Inches 

I 

r2 

I 

r2 

72 

8X/8 

3^X3 

3/8 

12.20 

115.9 

9.50 

25.7 

2.11 

73 

15.00 

142.1 

9:47 

34'.  7 

2.31 

74 

ft 

17.68 

166.4 

9.41 

43.5 

2.46 

75 

4      X3 

H 

12.92 

126.6 

9.79 

37.3 

2.89 

76 

16.00 

156.3 

9.77 

50.1 

3.13 

77 

$ 

18.92 

183.5 

9.70 

62.8 

3.32 

78 

5      X3 

y~ 

14.44 

148.7 

10.3 

70.2 

4.86 

79 

y*. 

18.00 

184.7 

10.3 

94.2 

5.24 

80 

ft 

21.44 

217.1 

10.1 

118.4 

5.52 

81 

X  3  5*2 

H 

15.20 

149.0 

9.80 

70.6 

4.64 

82 

19.00 

185.0 

9.74 

94.7 

4.99 

83 

¥ 

22.68 

218.3 

9.63 

118.2 

5.21 

84 

6      X3% 

16.68 

170.3 

10.2 

119.3 

7.15 

85 

y* 

21.00 

213.9 

10.2 

158.9 

7.57 

86 

ft 

25.20 

252.4 

10.0 

198.5 

7.88 

87 

29.24 

286.5 

9.80 

240.6 

8.23 

88 

8X*4 

3>£X2^ 

y* 

15.00 

146.6 

9.77 

36.1 

2.41 

89 

3y2x3  2 

y*. 

16.00 

147.4 

9.21 

36.7 

2.29 

90 

18  68 

171.7 

9.19 

46.2 

2.47 

91 

4      X3 

\/2 

17.00 

161.7 

9.51 

52.8 

3.10 

92 

ft 

19.92 

188.8 

9.48 

65.9 

3.31 

93 

5      X3 

19.00 

190.1 

10.00 

97.9 

5.15 

94 

ft 

22.44 

222.4 

9.91 

123.0 

5.48 

95 

5     X3^ 

20.00 

190.3 

9.52 

98.4 

4.92 

96 

ft 

23.68 

223.7 

9.44 

123.0 

5  19 

97 

X  3  5"2 

22.00 

219.2 

9.97 

164.2 

7.46 

98 

y& 

26.20 

257.8 

9.81 

204.9 

7.82 

99 

% 

30.24 

291.9 

9.65 

248.3 

8.21 

100 

9X# 

3      X2% 

% 

7.49 

95.5 

12.7 

10.3 

1.38 

101 

y& 

9.93 

129.6 

13.1 

15.7 

1  58 

102 

3*<2X2y2 

1A- 

8.01 

105.5 

13.2 

16.0 

2.00 

103 

H 

10.69 

144  0 

13.5 

24.2 

2.25 

104 

y2 

13.25 

179.5 

13.6 

32.3 

2.44 

34 


FOUR  ANGLES.        ONE  PLATE. 

(CONTINUED.) 

No. 

One  Web 
Plate, 
Size  in 
Inches 

FOUR  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  C.  D. 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

I 

r2 

105 

9X^ 

3^X3 

T5* 

9.97 

226.7 

22.7 

20.1 

2.02 

106 

YO 

11.45 

146.5 

12.8 

24  2 

2.12 

107 

I/ 

14.25 

181.7 

12.8 

32.8 

2.30 

108 

4      X3 

5 

10.61 

138.8 

13.1 

29.6 

2.79 

109 

3A 

12.17 

160.2 

13.2 

35.4 

2.91 

110 

^2 

15.25 

200.0 

13.1 

47.8 

3.13 

111 

5      X3 

A 

11.85 

162.2 

13.7 

56.3 

4.75 

112 

i2 

13.69 

188.5 

13.8 

67.6 

4.94 

113 

X 

17.25 

236.4 

13-7 

90.6 

5.25 

114 

5      X3J£ 

14.45 

189.6 

13.1 

67.9 

4.70 

115 

J^2 

18.25 

237.6 

13.0 

91.0 

4.99 

116 

6      X  3  5*2 

N 

15.93 

216.8 

13.6 

115.6 

7.26 

117 

20.25 

274.7 

13.6 

153.8 

7.60 

118 

6      X4 

A 

16.69 

217.8 

13.1 

115.4 

6.91 

119 

X 

21.25 

274.3 

12.9 

154.5 

7.27 

120 

9X2/6 

3      X2|^ 

y* 

11.06 

137.2 

12.4 

16.8 

1.52 

121 

3^X2/4 

11.82 

151.6 

12.8 

25.6 

2.17 

122 

' 

i/ 

14.38 

187.1 

13.0 

34.2 

2.38 

123 

3^X3 

y& 

12.58 

154.1 

12.3 

25.7 

2.05 

124 

i/ 

15.38 

189.3 

12.3 

34.7 

2.26 

125 

&£ 

18.06 

222  0 

12.3 

43.5 

2.41 

126 

4      X3 

H 

13.30 

167.8 

12.6 

37.3 

2.81 

127 

16.38 

207.6 

12.7 

50.1 

3.06 

128 

X 

19.30 

244.1 

12.7 

62.8 

3.26 

129 

5      X3 

14.82 

196.1 

13.2 

70.3 

4.74 

130 

K 

18.38 

244.0 

13.3 

94.2 

5.13 

131 

% 

21.82 

287.5 

13.2 

118.4 

5.42 

132 

5     X3  *-£ 

y% 

15.58 

197.2 

12.7 

70.6 

4.53 

133 

y> 

19.38 

245.2 

12.7 

94.7 

4.89 

134 

*A 

23.06 

290.1 

12.6 

118.2 

5.13 

135 

3/ 

26.62 

329.7 

12.4 

143.1 

5.38 

136 

5*2 

y 

17.06 

224.4 

13.2 

119.3 

6.99 

137 

\/ 

21.38 

282.3 

13.2 

158.9 

7.43 

138 

X 

25.58 

333.9 

13.1 

198.5 

7.76 

139 

* 

29.62 

380.4 

12.8 

240.6 

8.12 

140 

6      X4 

17.78 

225.4 

12.7 

119.3 

6.71 

141 

l/2 

22.38 

281.9 

12.6 

159.7 

7.14 

142 

26.82 

335.1 

12.5 

199.6 

7.44 

143 

*/£ 

31.14 

382.3 

12.3 

240.8 

7.73 

144 

9X^ 

3i^X2^ 

X 

15.50 

194.7 

12.6 

36.2 

2.33 

145 

3^X3 

16.50 

196.9 

11.9 

36.7 

2.22 

146 

ti 

19.18' 

229.6 

12.0 

46.2 

2.41 

35 


L  A  J 

FOUR   ANGLES.     C  ~?      i      J=^  D    ONE  PLATE. 
I            B           i 

No. 

One  Web 
Plate, 
Size  in 
Inches 

FOUR,  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  C.  D. 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

I 

r2 

147 

9X^ 

4      X3 

yz 

17.50 

215.2 

12.3 

52.8 

3.02 

148 

ft 

20.42 

251.7 

12.3 

65.9 

3.23 

149 

5      X3 

Yz 

19.50 

251.6 

12.9 

97.9 

5.02 

150 

ft 

22.94 

295.1 

12.9 

123.0 

5.36 

151 

5      X  3  5*2 

I/ 

20.50 

252.8 

12.3 

98.5 

4.80 

152 

ft 

24.18 

297.7 

12.3 

123.0 

5.09 

153 

y* 

27.74 

337.3 

12.2 

148.7 

5.36 

154 

51* 

22.50 

289.9 

12.9 

164.2 

7.30 

155 

ft 

26.70 

341.5 

12.8 

206.2 

7.72 

156 

X 

30.74 

388.0 

12.6 

248.3 

8.08 

157 

6      X4 

Yz 

23.50 

289.5 

12.3 

165.1 

7.02 

158 

27.94 

342.7 

12.3 

206.3 

7.38 

159 

34 

32.26 

389.9 

12.1 

248.9 

7.71 

160 

10x14: 

3*/2X2y2 

X 

8.26 

134.9 

16.3 

16.0 

1.94 

161 

3/8 

10.94 

184.2 

16.8 

24.2 

2.21 

162 

Yz 

13.50 

229.7 

17.0 

32.3 

2.39 

163 

3^X3 

TV 

10.22 

162.7 

15.9 

20.1 

1.97 

164 

H 

11.70 

188.2 

16.1 

24.2 

2.07 

165 

Yz 

14.50 

233.9 

16.1 

32.8 

2.26 

166 

4      X3 

10.86 

177.8 

16.4 

29.6 

2.72 

167 

H 

12.42 

205.1 

16.5 

35.4 

2.85 

168 

Yz 

15.50 

256.6 

16.6 

47.8 

3.08 

169 

5      X3 

_5T 

12.10 

207.0 

17.1 

56.3 

4.66 

170 

y^> 

13.94 

240.5 

17.3 

67.6 

4.85 

171 

i/ 

17.50 

302.1 

17.3 

90.6 

5.18 

172 

5      X3y2 

y% 

14.70 

242.7 

16.5 

67.9 

4.62 

173 

\/2 

18.50 

304.7 

16.5 

91.0 

4.92 

174 

6      X3J£ 

H 

16.18 

276.6 

17.1 

115.6 

7.15 

175 

Yz 

20.50 

350.8 

17.1 

153.9 

7.50 

176 

6      X4 

16.94 

278.4 

16.4 

115.4 

6.81 

177 

Yz 

21.50 

351.4 

16.4 

154.5 

7.19 

178 

IQXl/s 

3^X2^ 

y* 

12.19 

194.6 

16.0 

25.6 

2.10 

179 

Yz 

14.75 

240.1 

16.3 

34.2 

2.32 

FOUR  ANGLES.    ONE  PLATE. 

(CONTINUED.) 

fb. 

One  Web 
Plate, 
Size  in 
Inches 

FOUR  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  C.  D. 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

I 

r2 

180 

lOX^g 

3^X3 

3/8 

12.95 

198.6 

15.3 

25.7 

1.99 

181 

l/2 

15.75 

244.3 

15.5 

34.7 

2.20 

182 

ft 

18.43 

286.7 

15.6 

43.5 

2.36 

183 

4      X3 

3/S 

13.67 

215.5 

15.8 

37.3 

2.73 

184 

y* 

16.75 

267.0 

15.9 

50  1 

2.99 

185 

ft 

19.67 

314.3 

16.0 

62.8 

3.19 

186 

5      X3 

3/8 

15.19 

250.9 

16.5 

70.3 

4.62 

187 

i/ 

18.75 

312.5 

16.7 

94.2 

5.03 

188 

ft 

22.19 

368.8 

16.6 

118.4 

5.33 

189 

5      X3y2 

H 

15.95 

253.1 

15.9 

70.6 

4.42 

190 

19.75 

315.1 

16.0 

94.7 

4.80 

191 

ft 

23.43 

373.3 

15.9 

118.2 

5.05 

192 

6      X3^ 

f8 

17.43 

287.0 

16.5 

119.3 

6.85 

193 

21.75 

361.3 

16.6 

158.9 

7.31 

194 

ft 

25.95 

428.3 

16.5 

198.5 

7.65 

195 

34 

29.99 

489.2 

16.3 

240.6 

8.02 

196 

6      X4 

18.19 

288.8 

15.9 

119.3 

6.56 

197 

y* 

22.75 

361.8 

15.9 

159.7 

7.02 

198 

ft 

27.19 

430.8 

15.8 

199.6 

7.34 

199 

u 

31.51 

492.7 

15.6 

240.8 

7.64 

200 

10X^ 

3^X2^ 

l/2 

16.00 

250.5 

15.6 

36.2 

2.26 

201 

3^X3 

y2 

17.00 

254.7 

15.0 

36.7 

2.16 

202 

ft 

19.68 

297.2 

15.1 

46.2 

2.35 

203 

4      X3 

y 

18.00 

277.4 

15.4 

52.8 

2.93 

204 

ft 

20.92 

324.7 

15.5 

65.9 

3.15 

205 

5      X3 

yz 

20.00 

322.9 

16.1 

97.9 

4.90 

206 

ft 

23.44 

379.2 

16.2 

123.0 

5.25 

207 

5      X3*4 

21.00 

325.6 

15.5 

98.5 

4.69 

208 

s2 

24.68 

383.7 

15.6 

123.0 

4.98 

209 

6     X3% 

\/ 

23.00 

371.7 

16.2 

164.2 

7.14 

.    210 

ft 

27.20 

438.6 

16.1 

206.1 

7.58 

211 

H 

31.24 

499.6 

16.0 

248.3 

7.95 

212 

6      X4 

y^ 

24.00 

372.3 

15.5 

165.1 

6.88 

213 

ft 

28.44 

441.2 

15.5 

206.3 

7.25 

214 

32.76 

503.1 

15.4 

248.9 

7.60 

215 

12x14; 

3}£X2.^ 

% 

8.76 

206.4 

23.6 

16.0 

1.83 

216 

11.44 

281.1 

24.6 

24.2 

2.11 

217 

y2 

14.00 

350.4 

25.0 

32.3 

2.31 

218 

3^X3 

5 
T  T 

10.72 

250.3 

23.4 

20.2 

1.88 

219 

3/8 

12.20 

289.3 

23.7 

24.2 

1.99 

220 

i    'V-z       15.00 

359.8 

24.0 

32.8 

2.19 

37 


1    A    1 

FOUR   ANGLES.    C  ==£—•.-—=  D    ONE  PLATE. 

No. 

One  Web 
Plate, 
Size  in 
Indies 

FOUR  ANGLES 

Total 
Area, 
Square 
Indies 

AXIS  A.  B. 

AXIS  C,  D. 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

I 

r2 

221 

12X^ 

4     X3 

A 

11.36 

272.2 

24.0 

29.6 

2.60 

222 

H 

12.92 

314.0 

24.3 

35.4 

2.74 

223 

16.00 

393:2 

24.6 

47.8 

2.99 

224 

5     X3 

T& 

12.60 

314.7 

25.0 

56.4 

4.47 

225 

y& 

14.44 

365.5 

25.3 

67.6 

4.68 

226 

y*. 

18.00 

459.7 

25.5 

90.6 

5.03 

227 

5     ^3/^ 

y& 

15.20 

371.1 

24.4 

67.9 

4.46 

228 

'A 

19.00 

466.8 

24.6 

91.0 

4.79 

229 

6      X3J^ 

H 

16.68 

420.6 

25.2 

115.6 

6.93 

230 

21.00 

534.2 

25.4 

153.9 

7.33 

231 

6      X4 

Vt, 

17.44 

425.3 

24.4 

115.4 

6.62 

232 

y* 

22.00 

538.0 

24.5 

154.6 

7.03 

233 

12X^ 

3^X2^ 

y% 

12.94 

299.1 

23.1 

25.7 

1.98 

234 

l/2 

15.50 

368.4 

23.8 

34.2 

2.21 

235 

3^X3 

3/8 

13.70 

307.3 

22.4 

25.7 

1.88 

236 

16.50 

377.8 

22.9 

34.7 

2.10 

237 

% 

19.18 

443.9 

23.2 

43.5 

2.27 

238 

4      X3 

y& 

14.42 

332,0 

23.0 

37.3 

2.59 

239 

y* 

17.50 

411  2 

23.5 

50.2 

2.87 

240 

$ 

20.42 

484.5 

23.7 

62.9 

3.08 

241 

5      X3 

H 

15.94 

383.5 

24.1 

70.3 

4.41 

242 

19.50 

477.7 

24.5 

94.3 

4.83 

243 

fa 

22.94 

564.9 

24.6 

118.4 

5.16 

244 

5      X3^ 

y* 

16.70 

389.1 

23.3 

70.6 

4.23 

245 

20.50 

484.8 

23.6 

94.7 

4.62 

246 

fa 

24.18 

575.1 

23.8 

118.2 

4.89 

247 

6      X3  1£ 

y& 

18.18 

438.6 

24.1 

119.3 

6.56 

248 

y* 

22.50 

552.2 

24.5 

158.9 

7.06 

249 

fa 

26.70 

656.2 

24.6 

198.5 

7.43 

250 

30.74 

751.7 

24.5 

240.6 

7.83 

251 

6      X4 

y* 

18.94 

443.3 

23.4 

119.3 

6.30 

252 

23.50 

556.0 

23.7 

159.7 

6.80 

253 

fa 

27.94 

663.1 

23.7 

'199.7 

7.15 

254 

32.26 

760.8 

23.6 

240.8 

7.46 

38 


FOUR  ANGLES.    ONE  PLATE.     (CONTINUED.) 

No. 

One  Web 
Plate, 
Size  in 
Inches 

FOUR  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  C.  D. 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

I 

r2 

255 

12X^ 

3^jX2^ 

y* 

17.0 

386.4 

22.7 

36.2 

2.13 

256 

3^X3 

% 

18.0 

395.8 

22.0 

36.7. 

2.04 

257 

20.68 

461.9 

22.3 

46.2 

2.23 

258 

4      X3 

\s 

19.00 

429.2 

22.6 

52.8 

2.78 

259 

$ 

21.92 

502.5 

22.9 

66.0 

3.01 

260 

5     X3 

l/t 

21.00 

495.7 

23.6 

97.9 

4.66 

261 

% 

24.44 

582.9 

23.9 

123.1 

5.04 

262 

5     X3^ 

l/2 

22.00 

502.8 

22.9 

98.5 

4.48 

263 

yk 

25.68 

593.1 

23.1 

123.0 

4.79 

264 

6      X3j^ 

\/ 

24.00 

570.2 

23.8 

164.2 

6-84 

265 

y* 

28.20 

674.2 

23.9 

206.1 

7.31 

266 

*4 

32.24 

769.7 

23.9 

248.3 

7.70 

267 

6     X4 

% 

25.00 

574.0 

23.0 

165.1 

6.60 

268 

% 

29.44 

681.1 

23:i 

206.3 

7.01 

269 

& 

33.76 

778.8 

23.1 

248.9 

7.37 

270 

14Xi^ 

4      X3 

TS" 

11.86 

389.3 

32.8 

29.6 

2.49 

271 

If 

13.42 

448.7 

33.4 

35.4 

2.64 

272 

16.50 

561.8 

34.0 

47.8 

2.90 

273 

5      X3 

T5F 

13.10 

447.6 

34.2 

56.4 

.30 

274 

3/ 

14.94 

519.4 

34.8 

67.6 

.52 

275 

l/2 

18.50 

653.4 

35.3 

90  6 

.90 

276 

5      X3^ 

y% 

15.70 

529.8 

33.7 

67.9 

.32 

277 

19.50 

666.8 

34.2 

91.0 

.67 

278 

6      X3^ 

3/8 

17.18 

598.0 

34.8 

115.6 

6.73 

279 

21.50 

759.4 

35.3 

153.9 

7.16 

280 

6      X4 

H 

17.94 

607.1 

33.8 

115.4 

6.43 

281 

*/2 

22.50 

768.6 

34.2 

154.6 

6.87 

282 

14X^g 

4      X3 

f' 

15.17 

477.2 

31.5 

37.3 

2.46 

283 

18.25 

590.4 

32.4 

50.2 

2.75 

284 

5^ 

21.17 

695.5 

32.9 

62.9 

2.97 

285 

5      X3 

y% 

16.69 

548.0 

32.8 

70.3 

4.21 

286 

l/2 

20.25 

682  0 

33.7 

94.3 

4.66 

287 

R/ 

23.69 

806.8 

34.1 

118.4 

5.00 

288 

5      X3^ 

y% 

17.45 

558.4 

32.0 

70.6 

4.04 

289 

% 

21.25 

695.3 

32.7 

94.7 

4.46 

290 

24.93 

825.4 

33.1 

118.2 

4.74 

291 

6      X3^ 

y% 

18.93 

626.6 

33.1 

119.4 

6.30 

292 

y 

23.25 

788.0 

33.9 

158.9 

6  84 

293 

e£ 

27.45 

937.6 

34.2 

198.5 

7.23 

294 

\ 

31.49 

1075.9 

34.2 

240.6 

7.64 

295 

6      X4 

y% 

19.69 

635.6 

32.3 

119.4 

6.06 

296 

y* 

24.25 

797.1 

32.9 

159.7 

6.59 

297 

28.69 

951.2 

33.2 

199.7 

6.96 

298 

y* 

33.01 

1093.4 

33.1 

240,8 

7.29 

1    A  J 

FOUR  ANGLES       c  CS            SJ  D    ONE  PLATE- 

1            B           1 

No. 

One  Web 
Plale,  - 
Size  in 
Inches 

FOUR  ANGLES 

Total 
Are«, 
Square 
Inches 

AXIS  A.  B. 

AXIS  0.  I). 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

I 

r2 

2^9 

14X^ 

4      X3 

Yz 

20.00 

618.9 

31.0 

52.9 

2.64 

300 

y$> 

22.92 

724.1 

31.6 

66.0 

2.88 

301 

5     X3 

y> 

22.00 

710.6 

32.3 

98.0 

4.45 

302 

y% 

25.44 

835.4 

32.8 

123.1 

4.84 

303 

5     X3;^ 

K 

23.00 

723.9 

31.5 

98.5 

4.28 

304 

y% 

26.68 

854.0 

32.0 

123.1 

4.61 

305 

6      X3^ 

i/-> 

25.00 

816.5 

32.7 

164.3 

6.57 

306 

H 

29.20 

966.2 

33.1 

206.1 

7.06 

307 

33.24 

1104.5 

33.2 

248.3 

7.47 

308 

6      X4 

H 

26.00 

825.7 

31.8 

165.1 

6.35 

309 

^8 

30.44 

979.8 

32.2 

206.3 

6.78 

310 

3^ 

34.76 

1122.0 

32.3 

248.9 

7.16 

311 

16X^" 

5      X3    • 

A 

13.60 

606.7 

44.6 

56.4 

4.14 

312 

y& 

15.44 

703.1 

45.5 

67.6 

4.38 

313 

i/. 

19.00 

884.1 

46.5 

90.6 

4.77 

314 

5      X3^ 

y% 

16.20 

720.0 

44.4 

67.9 

4.19 

315 

1A 

20.00 

905.8 

45.3 

91.0 

4.55 

316 

6      X3/4 

^8 

17.68 

809.8 

45.8 

115.6 

6.54 

317 

l/t 

22.00 

1027.6 

46.7 

153.9 

6.99 

318 

6      X4 

y* 

18.44 

824.6 

44.7 

115.4 

6.26 

319 

l/2 

23.00 

1043.9 

45.4 

154.6 

6.72 

320 

16X^ 

5      X3 

H 

17.44 

745.8 

42.8 

70.3 

4.03 

321 

y^ 

21.00 

926.7 

44.1 

94.3 

4.49 

322 

y§ 

24.44 

1096.1 

44.9 

118.4 

4.84 

323 

5      X3l£ 

y% 

18.20 

762.7 

41.9 

70.6 

3.88 

324 

yz 

22.00 

948.5 

43.1 

94.8 

4.31 

325 

y& 

25.68 

1125.5 

43.8 

118.3 

4.61 

326 

6      X3^ 

y* 

19.68 

852.5 

43.3 

119.4 

6.07 

327 

y* 

24.00 

1070.3 

44.6 

159.0 

6.62 

328 

28.20 

1273.7 

45.2 

198.5 

7.04 

329 

*/i 

32.24 

1463.0 

45.4 

240.6 

7  46 

330 

6      X4 

H 

20.44 

867.3 

42.4 

119.4 

5.84 

331 

25.00 

1086.6 

43.5 

159.7 

6.39 

332 

ft 

29.44 

1296.8 

44.1 

199.7 

6.78 

333 

H 

33.76 

1492.0 

44.2 

240.8 

7.13 

FOUR  ANGLES.        ONE  PLATE. 

(CONTINUED.) 

One  Web 

FOUR  ANCLES 

Total 

AXIS  A.  B. 

AXIS  C.  D. 

No. 

Plate, 

Size  in 
Inches 

Size  in 
Incises 

Thick- 
ness 

Area, 
Square 
Inches 

I 

r2 

I 

r2 

334 

IBXfl 

5     X3 

y* 

23.00 

969.4 

42.1 

98.0 

4.28 

335 

H 

26.44 

1138.8 

43.1 

123.1 

4.63 

336 

5     X3'/2 

% 

24.00 

991.2 

41.3 

98.5 

4.11 

337 

H 

27.68 

1168.1 

42.2 

123.1 

4.45 

338 

6     X3^ 

l/2 

26.00 

1112.9 

42.8 

1,64.3 

6.32 

339 

X 

30.20 

1316.3 

43.6 

206.1 

6.83 

340 

X 

34.24 

1505.6 

44.0 

248.4 

7.25 

341 

6      X4 

y* 

27.00 

1129.3 

41.8 

165.2 

6.12 

342 

H 

31.44 

1339.5 

42.6 

206.3 

6.56 

343 

3A 

35.76 

1534.7 

42.9 

248.9 

6.96 

344 

18XX 

6      X3^ 

ft 

18.18 

1057.0 

58.1 

115.6 

6.36 

345 

% 

22.50 

1340.0 

59.6 

153.9 

6.84 

346 

6      X4 

ft 

18.94 

1079  0 

57.0 

115.4 

6.09 

347 

X 

23.50 

1366.0 

58.1 

154.6 

6.58 

348 

18X^ 

6      X3^ 

y* 

20.43 

1118.0 

54.7 

119.4 

5.84 

349 

X 

24.75 

1401. 

56.6 

159.0 

6.42 

350 

H 

28.95 

1666. 

57.6 

198.5 

6.86 

351 

X 

32.99 

1914. 

58.0 

240.7 

7.29 

352 

6     X4 

# 

21.19 

1140. 

53.8 

119.4 

5.63 

353 

l/2 

25.75 

1426. 

55.4 

159.7 

6  20 

354 

% 

30.19 

1701. 

56.4 

199.7 

6.61 

355 

X 

34.51 

1958. 

56.8 

240.8 

6.98 

356 

8      X6 

% 

33.79 

1802. 

53.3 

368.9 

10.9 

357 

% 

40.51 

2173. 

53.7 

468.7 

11.6 

358 

K 

46.51 

2490. 

53.4 

563.1 

12.1 

359 

'7/$ 

53.23 

2838. 

53.3 

672.2 

12.6 

360 

i 

60.39 

3192. 

52.9 

811.6 

13.4 

361 

18X^ 

6     X3>£ 

% 

27.00 

1462. 

54.1 

164.3 

6.09 

362 

ft 

31.20 

1727. 

55.4 

206.2 

6.61 

363 

^ 

35.24 

1975. 

56.1 

248.4 

7.05 

364 

6      X4 

% 

28.00 

1487. 

53.1 

165.2 

5.90 

365 

ft 

32.44 

1762. 

54.3 

206.4 

6.36 

366 

% 

36.76 

2019. 

54.9 

249.0 

6.77 

367 

8      X6 

y* 

36.04 

1863. 

51.7 

377.8 

10.5 

368 

% 

42.76 

2234. 

52.3 

479.9 

11.2 

369 

X 

48.76 

2551. 

52.3 

576.7 

11.8 

370 

7/& 

55.48 

2899. 

52.3 

688.2 

12.4 

371 

i 

62.64 

3253. 

51.9 

830.7 

13.3 

i  °  r 

TWO  PLATES.         A  |  Ifi        FOUR  ANGLES. 

j|  D!L 

Two  Web 

FOUR  ANGLES 

Total 

AXIS  A.  B. 

AXIS  0.  D. 

No. 

Plates, 
Size  in 
Inches 

Size  in 
Inches 

Thick- 
ness 

Area, 
Square 
Inches 

I 

r2 

Out  to 
Out  of 
Webs 

I 

1 

8XX 

2      X2 

X 

7.76 

66.5 

8.57 

5.4 

68.5 

2 

5_ 

8.60 

75.9 

8.82 

3 

y» 

9.44 

84.7 

8.97 

5.4 

89.0 

4 

8xT5<r 

2      X2 

* 

9.60 

81.2 

8.46 

5.3 

81.6 

5 

y% 

10.44 

90.0 

8.62 

6 

A 

11.24 

98.4 

8.76 

5.3 

102. 

7 

9XX 

iys**ji 

1A 

9.26 

101. 

10.9 

5.9 

103. 

8 

JL 

10.38 

117. 

11.3 

9 

H 

11.42 

131. 

11.5 

.  5.9 

135. 

10 

9XT5T 

2%X2y2 

jL 

11.51 

124. 

10.8 

5.9 

127. 

11 

y% 

12.55 

139. 

11.1 

12 

T'O 

13.63 

153. 

11.2 

5.9 

160. 

13 

ioxx 

3      X2^ 

x 

10.24 

143. 

14.0 

6.5 

144. 

14 

r> 
TiT 

11.48 

166. 

14.5 

15 

jtf 

12.68 

187. 

14.8 

6.5 

191. 

16 

loxrV 

3      X2  \"i. 

r, 
i  (> 

12.73 

177. 

13.9 

6.5 

179. 

17 

13.93 

198. 

14.2 

18 

7 
Ttf 

15.13 

219. 

14.5 

6.4 

221. 

19 

10X^ 

3      X2^ 

# 

15.18 

208. 

13.7 

6.5 

213. 

20 

7 

16.38 

229. 

14.0 

21 

I/ 

17.50 

248. 

14.2 

22 

A 

18.62 

267. 

14.3 

6.3 

268. 

23 

12X^ 

3      X3 

X 

11.76 

230. 

19.6 

8.1 

235. 

24 

ij 

13.12 

265. 

20.2 

25 

k 

14.44 

299. 

20.7 

8.1 

305. 

26 

12XT56 

3      X3 

A 

14.62 

283. 

19.4 

8.0       286. 

27 

fy& 

15.94 

317. 

19.9 

28 

T7^ 

17.22 

350. 

20.3 

29 

s 

18.50 

382. 

20.6 

8.0       387. 

TWO  PLATES.      FOUR  ANGLES. 

(CONTINUED.) 

No. 

Two  Web 
Plates, 
Size  in 
Inches 

FOUR  ANCLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  C.  D. 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

Out  to 
Out  of 
Webs 

I 

30 

12X3/8 

3      X3 

H 

17.44 

335. 

19.2 

8.0 

340. 

31 

A 

18.72 

368. 

19.6 

32 

20.00 

400. 

20.0 

33 

9 

21.24 

430. 

20.2 

34 

H 

22.44 

457. 

20.4 

7.9 

464. 

35 

12X^ 

3      X3 

K 

23.00 

436. 

18.9 

8.0 

445. 

36 

9 

24.24 

466. 

19.2 

37 

>l 

25.44 

493. 

19.4 

7.9 

502. 

38 

12X^£ 

3      X3 

ft 

28.44 

529. 

18.6 

7.9 

536. 

39 

12XX 

3>£X2J4 

l£ 

11.76 

242. 

20.6 

8.0 

248. 

40 

5 
TtT 

13.12 

280. 

21.4 

41 

H 

14.44 

317. 

22.0 

42 

A 

15.72 

352. 

22.4 

7.9 

355. 

43 

12xiV 

3J4X2J4 

A 

14.62 

298. 

20.4 

7.9 

301. 

44 

y* 

15.94 

335. 

21.0 

45 

T'*T 

17.22 

370. 

21.5 

46 

§ 

18.50 

404. 

21.9 

7.9 

412. 

47 

12X^/8 

3J4X2I4 

N 

17.44 

353. 

20.2 

7.9 

358. 

48 

A 

18.72 

388. 

20.7 

49 

20.00 

422. 

21.1 

50 

» 

22.44 

485. 

21.6 

7.7 

486. 

51 

12XJ4 

3^X2^ 

14 

23.00 

458. 

19.9 

7.8 

459. 

52 

9,. 

24.24 

490. 

20.2 

53 

^ 

25.44 

521. 

20.5 

7.8 

532. 

54 

12X# 

314x214 

# 

28.44 

557. 

19.6 

7.8 

566. 

55 

14XT\ 

3J4X3>£ 

A 

17.11 

455. 

26.6 

9.4 

461. 

56 

ft 

18.67 

510. 

27.3 

57 

20.23 

564. 

27.9 

56 

^ 

21.75 

616. 

28.3 

9.4 

626. 

59 

14X3/8" 

314x314 

r^ 

20.42 

539. 

26.4 

9.4 

549. 

60 

A 

21.98 

592. 

26.9 

61 

23.50 

645. 

27.4 

62 

^ 

26.42 

743. 

28.1 

9.3 

753. 

63 

14X^ 

3^X3^ 

yz 

27.00 

702. 

26.0 

9.3 

710. 

64 

_9 

28.48 

752. 

26.4 

65 

^ 

29  92 

800. 

26.7 

9.3 

815. 

~ii  c  sr 

TWO  PLATES.       A  f  —1-6      FOUR   ANGLES. 
J    DJL 

No. 

Two  Web 
Plates, 
Size  in 
Inches 

FOUR  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  C.  D. 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

Out  to 
Out  of 
Webs 

I 

66 

14XJ* 

3^X3^ 

% 

33.42 

857. 

25.7 

9.2 

857. 

67 

14X3^ 

314x3% 

X 

34.00 

816. 

24.0 

9.3 

822. 

68 

A 

35.  4b 

866. 

24.4 

69 

A 

36.92 

914. 

24.8 

9.3 

927. 

70 

14  X  A 

4      X3 

A 

17.11 

475. 

27.8 

9.2 

482. 

71 

3/£ 

18.67 

534. 

28.6 

72 

JL 

20.23 

593. 

29.3 

73 

l/2 

21.75 

648. 

29.8 

9.2 

650. 

74 

14X3^ 

4      X3 

N 

20.42 

563. 

27.6 

9.2 

563. 

75 

A 

21.98 

622. 

28.3 

76 

23.50 

676. 

28.8 

77 

M 

26.42 

781. 

29.6 

9.2 

796. 

78 

14Xl£ 

4      X3 

y2 

27.00 

733. 

27.2 

9.2 

742. 

79 

A 

28.48 

787. 

27.6 

80 

H 

29.92 

838. 

28.0 

9.1 

841. 

81 

14X# 

4      X3 

>8 

33.42 

896. 

26.8 

9.1 

897. 

82 

14X34 

4      X3 

14 

34.00 

848. 

24.9 

9.2 

852. 

83 

A 

35.48 

901. 

25.4 

84 

H 

36.92 

953. 

25.8 

9.2 

966. 

85 

15XT7 

3^X3^ 

& 

17.74 

540. 

30.4 

10.2 

549. 

86 

& 

19.30 

605. 

31.4 

87 

A 

20.86 

668. 

32.0 

88 

22.38 

729. 

32.6 

10.2 

737. 

89 

15X3/8 

3y2X3y2 

Hi 

21.17' 

640. 

30.2 

10.1 

642. 

90 

T% 

22.73 

703. 

30.9 

91 

i£ 

24.25 

765. 

31.5 

92 

y& 

27.17 

880. 

32.4 

10.1 

885. 

93 

15X^ 

3^X3^ 

y* 

28.00 

835.  ' 

29.8 

10.1 

846. 

94 

A 

29  48 

894. 

30.3 

95 

H 

30.92 

951... 

30.7 

10.1 

965. 

TWO  PLATES.     FOUR  ANGLES.     (CONTINUED.) 

No. 

Two  Web 
Plates, 
Size  in 
Inches 

FOUR  ANGLES 

Total 
Area, 
Square 
Inches  . 

AXIS  A.  B. 

AXIS  C.  D. 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

Out  to 
Out  of 
Webs 

I 

96 

15X^    j    3/2X3% 

X 

34.67 

1021. 

29.4 

10.0 

1023. 

97 

15X3/       3  14  X3  l/t 

i£ 

35.50 

976. 

27  5 

10.1 

992. 

98 

Tfi 

36.98 

1035. 

28.0 

99 

& 

38.42 

1091. 

28.4 

10.1 

1111. 

100 

15X^6 

3^X3^ 

39.25 

1046. 

26.6 

10.1 

1059. 

101 

9 

40.73 

1105. 

27.1 

102 

ft 

42.17 

1162. 

27.5 

10.1 

1179. 

103 

15X& 

4      X3 

A 

17.74 

562. 

31.7 

10.1 

571. 

104 

H 

19.30 

631. 

32.7 

105 

A 

20.86 

700. 

33.5 

106 

X 

22.38 

764. 

34.1 

10.1 

774. 

107 

15X3/6 

4      X3 

y^ 

21.17 

667. 

31.5 

10.0 

668. 

108 

7 

22.73 

735. 

32.3 

109 

X 

24.25 

799. 

33.0 

110 

ft 

27.17 

922. 

33.9 

10.0 

931. 

111 

15X^4 

4      X3 

X 

28.00 

869. 

31.1 

10.0 

880. 

112 

29.48 

932. 

31.6 

113 

II 

30.92 

993. 

32.1 

10.0 

1009. 

114 

15X# 

4      X3 

X 

34.67 

1063. 

30.7 

9.9 

1064. 

115 

15X3^ 

4      X3 

X 

35.50 

1010. 

28.5 

10.0 

1022. 

116 

36.98 

1073. 

29.0 

117 

X 

38.42 

1133. 

29.5 

10.0 

1151. 

118 

15X^5 

4      X3 

y* 

39.25 

1080. 

27.5 

10.0 

1089. 

119 

40.73 

1143. 

28.1 

120 

ft 

42.17 

1203. 

28.5 

10.0 

1218. 

121 

16X3/£ 

3^X3^ 

y* 

21.92 

752. 

34.3 

10.9 

758. 

122 

j 

23.48 

825. 

35.1 

123 

y 

25.00 

897. 

35.9 

124 

ft 

27.92 

1031. 

36.9 

10.9 

1032. 

125 

16Xi^ 

3%X3]4 

X 

29.00 

982. 

33.9 

10.9 

998. 

126 

A 

30.48 

1051. 

34.5 

127 

ft 

31.92 

1117. 

35.0 

10.9 

1133. 

128 

16X^ 

3y2X3% 

ft 

35.92 

1200. 

33.5 

10.8 

1210. 

129 

16X3^ 

3*4X3% 

y* 

37.00 

1155. 

31.2 

10.8 

1165. 

130 

A 

38.48 

1220. 

31.7 

131 

ft 

39.92 

1285. 

32.2 

10.8 

1295. 

132 

16XJ£ 

3)4X3% 

X 

41.00 

1240. 

30.2 

10.8 

1250. 

133 

A 

42.48 

1305. 

30.8 

134 

43.92 

1375. 

31.3 

10.8 

1380. 

45 


1?  F 

TWO  PLATES.       A-f-j—  1-6      FOUR  ANGLES. 

J  b  L 

No. 

Two  Web 
Plates, 
Size  in 
Inches 

FOUR  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  C.  D. 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

Out  to 
Out  of 
Webs 

I 

135 

16X1 

3^X3^ 

# 

45.00 

1325. 

29.4 

10.8 

1330. 

136 

T7T 

46.48 

1390. 

30.0 

137 

H 

47.92 

1460. 

30.4 

10.8 

1460. 

138 

16X^ 

4      X3 

3/s 

21.92 

780. 

35.6 

10.8 

785. 

139 

TE 

23.48 

860. 

36.6 

140 

tt 

25.00 

935. 

37.4 

141 

H 

27.92 

1075. 

38.6 

10.8 

10SO. 

142 

16X^ 

4      X3 

y* 

29.00 

1020. 

35.1 

10.8 

1035. 

143 

JL 

30.48 

1090. 

35.8 

144 

H 

31.92 

1160. 

36.4 

10.8 

1180. 

145 

16X^ 

4      X3 

# 

35.92 

1245. 

34.7 

10.7 

1250. 

146 

16X^ 

4      X3 

Yi 

37.00 

1190. 

32.2 

10.7 

1195'. 

147 

JL 

38.48 

1265. 

32.8 

148 

8 

39.92 

1335. 

33.4 

10.7 

1335. 

149 

16X^ 

4      X3 

y* 

41.00 

1275. 

31.1 

10.7 

1275. 

150 

A 

42.48 

1350. 

31.7 

151 

H 

43.92 

1420. 

32.3 

10.7 

1420. 

152 

16X1 

4      X3 

% 

45.00 

1360. 

30.2 

10.8 

1380. 

153 

Yff 

46.48 

1435. 

30.8 

154 

)l 

47.92 

1505. 

31.4 

10.8 

1525. 

155 

18X^ 

3^X3^ 

/8 

23.42 

1010. 

43.1 

12.4 

1015. 

156 

17J 

24.98 

1105. 

44.2 

157 

26.50 

1200. 

45.2 

158 

^ 

29.42 

1375. 

46.8 

12.6 

1398.' 

159 

18X^ 

3^X3^ 

^ 

31.00 

1320. 

42.6 

12.4 

1335. 

160 

T7) 

32.48 

1410. 

43  4 

161 

33.92 

1495. 

44.1 

12.4 

1505, 

46 


TWO  PLATES.        FOUR  ANGLES. 

(CONTINUED.) 

Two  Web 

FOUR  ANGLES 

Total 

AXIS  A.  B. 

AXIS  C.  D. 

No. 

Plates, 
Size  in 
Inches 

Size  in 
Inches 

Thick- 
ness 

Area, 
Square 
Inches 

I 

r2 

Out  to 
Out  of 
Webs 

I 

162 

iQxfy 

3%X3% 

# 

38.42 

1620. 

42.1 

12.3 

1620. 

163 

18X%( 

3^X3^ 

yt 

40.00 

1565. 

39.1 

12.2 

1565. 

164 

T9<T 

41.48 

1655. 

39.9 

165 

R 

42.92 

1740. 

40.5 

12.3 

1755. 

166 

18X1 

3yx3U 

2 

y* 

49.00 

1805. 

36.9 

12.2 

1815. 

167 

i9,c 

50.48 

1895. 

37.6 

168 

51.92 

1985. 

38.2 

12.3 

2005. 

169 

18X^ 

5      X3y^ 

•fa 

25.70 

1185. 

46.1 

12.0 

1195. 

170 

i"V 

27.62 

1310. 

47.4 

171 

% 

29.50 

1430. 

48.4 

172 

$ 

33.18 

1660. 

50.0 

12.0 

1670. 

173 

18XJ£ 

5      X3l£ 

% 

34.00 

1550. 

45.6 

11.9 

1550. 

174 

T9,T 

35.88 

1670. 

46.5 

175 

* 

X 

37.68 

1780. 

47.3 

11.9 

1785. 

176 

18X^ 

5      X3  fy 

ji 

42.18 

1900. 

45.1 

11.9 

1915. 

177 

18X^ 

5     X3j4 

X 

43.00 

1790. 

41.7 

11.9 

1805. 

178 

44.88 

1910. 

42.6 

179 

V 

46.68 

2025. 

43.3 

11.9 

2040. 

180 

18X1 

5      X3}4 

y* 

52.00 

2035. 

39.1 

11.9 

2040. 

181 

A 

53.88 

2155. 

40.0 

182 

% 

55.68 

2265. 

40.7 

11.9 

2270. 

183 

21X^4 

4      X4 

y* 

27.19 

1600. 

58.8 

14.5 

1610. 

184 

JL 

28.99 

1755. 

60.5 

185 

* 

30.75 

1905. 

61.9 

186 

34.19 

2190. 

64.1 

14.7 

2190. 

187 

21X^ 

4      X4 

yz 

36.00 

2095. 

58.3 

14.5 

2120. 

188 

37.72 

2240. 

59.4 

189 

39.44 

2385. 

60.4 

14.6 

2415. 

190 

21X^ 

4      X4 

H 

44.69 

2575. 

57.6 

14.4 

2585. 

191 

2ix^ 

4      X4 

yz 

46.50 

2485. 

53.4 

14.3 

2510. 

192 

9T 

48.22 

2625. 

54.4 

193 

& 

49.94 

2770. 

55.5 

14.4 

2805. 

194 

21X1 

4      X4 

y* 

57.00 

2870. 

50.3 

14.2 

2885. 

195 

JL 

58.72 

3010. 

51.3 

196 

5A 

60.44 

3155. 

52.2 

14.3 

3180. 

47 


lcr 

TWO  PLATES.         A.l  --.LB        FOUR  ANGLES. 

J    D    L 

So. 

Two  Web 
Plates, 
Size  in 
Inches 

FOUR  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  C.  D. 

Size  in 
Inches 

Thick- 
ness 

.    I 

r2 

Out  to 
Out  of 
Webs 

I 

197 

21x114: 

4X4 

1A 

67.50 

3255. 

48.2 

14.2 

3255. 

198 

A 

69.22 

3395. 

49.1 

199 

70.94 

3540. 

49.9 

14.3 

3560. 

200 

21X1# 

4X4 

y2 

78.00 

3640. 

46.7 

14.3 

3655. 

201 

T9(T 

79.72 

3785. 

47.5 

202 

H- 

81.44 

3925. 

48.2 

14.4 

3970. 

203 

24  X   T^ 

4X4 

K 

36.00 

2785. 

77.4 

16.8 

2805. 

204 

T\ 

37.72 

2960. 

79.0 

205 

n 

39.44 

3175. 

80.5 

16.9 

3175. 

206 

24X    yz 

4X4 

yz 

39.00 

2930. 

75.1 

16.7 

2960. 

207 

9r 

40.72 

3125. 

76.7 

208 

H 

42.44 

3320. 

78.2 

16.8 

3330. 

209 

24  X    ft 

4X4 

% 

48.44 

3605. 

77.4 

16.6 

3615. 

210 

24X    % 

4X4 

yz 

51.00 

3505. 

66.8 

16.4 

3545. 

211 

y'g- 

52.72 

3700. 

70.2 

212 

H 

54.44 

3895. 

71.5 

16.5 

3915. 

213 

24X1 

4X4 

y* 

63.00 

4080. 

64.8 

16.2 

4090. 

214 

9 

64.72 

4275. 

66.1 

215 

ISA 

66.44 

4470. 

67.3 

16.4 

4515. 

216 

24X1»^ 

4X4 

1A 

75.00 

4660. 

62.1 

16.2 

4670. 

217 

A 

76.72 

4850. 

63.2 

218 

8 

78.44 

5045. 

64.3 

16.3 

5050. 

219 

24yl>^ 

4X4 

i/ 

87.00 

5235. 

60.2 

16.3 

5285. 

220 

A 

88.72 

5425. 

61.2 

221 

90.44 

5620. 

62.2 

16.4 

5675. 

222 

27X    y2 

4X4 

^ 

42.00 

3940. 

93.8 

18.8 

3960. 

223 

T'ff 

43.72 

4190. 

95.8 

224 

fl 

45.44 

4445 

97.8 

19.0 

4460. 

225 

27X    ft 

4X4 

5/8 

52.19 

4855. 

93.0 

18.8 

4900. 

4S 


TWO  PLATES.      FOUR  ANGLES. 

(CONTINUED.) 

No. 

Two  Web 
Plates, 
Size  in 
Inches 

FOUR  ANGLES 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  0,  D. 

Size  in 
Inches 

Thick- 
ness 

I 

r2 

Ont  to 
Out  of 
Webs 

I 

226 

27  X   ^ 

4X4 

X 

55.50 

4760. 

85.8 

18.4 

4790. 

227 

T5 

57.22 

5010. 

87.6 

228 

ft 

58.94 

5265. 

89.3 

18.6 

5295. 

229 

27X1 

4X4 

X 

69.00 

5580. 

80.9 

18.2 

5605. 

230 

T9* 

70.72 

5830. 

82.4 

231 

X 

72.44 

6085. 

84.0 

18.4 

6125. 

232 

27X1*4 

4X4 

X 

85.94 

6905. 

80.3 

18.3 

6920. 

233 

27X1% 

4x4 

ft 

99.44 

7725. 

77.7 

18.3 

7745. 

234 

27X   y2 

6X6 

y* 

50.00 

4935. 

98.7 

18.4 

4965. 

235 

ft 

55.44 

5675. 

102.4 

236 

X 

60.76 

6390. 

105.2 

237 

65.96 

7080. 

107.4 

18.5 

7090. 

238 

27X   ft 

6X6 

ft 

62.19 

6085. 

97.9 

18.3 

6100. 

239 

67.51 

6800. 

100.7 

240 

% 

72.71 

7495. 

103.1 

241 

i 

77.75 

8155. 

104.9 

18.4 

8190. 

242 

27X   % 

6X6 

ft 

68.94 

6495. 

94.2 

18.2 

6515. 

243 

H 

74.26 

7210. 

97.1 

244 

X 

79.46 

7905. 

99.5 

245 

i 

84.50 

8565. 

101.3 

18.3 

8595. 

246 

27X    7/% 

6X6 

* 

75.69 

6905. 

91.3 

18.1 

6910. 

247 

81.01 

7620. 

94.1 

248 

y* 

86.21 

8315. 

96.4 

249 

i 

91.25 

8975. 

98.3 

18.3 

9065. 

250 

27X1 

6X6 

ft 

82.44 

7315. 

88.8 

18.1 

7355. 

251 

87.76 

8030. 

91.5 

252 

#* 

92.96 

8725. 

93.8 

253 

i 

98.00 

9385. 

95.8 

18.2 

9425. 

254 

27X1^ 

6X6 

ft 

95.94 

8135. 

84.8 

18.1 

8195. 

255 

101.26 

8850. 

87.4 

256 

y* 

106.46 

9545. 

89.6 

257 

i 

111.50 

10205. 

91.5 

18.2 

10280. 

258 

27X1*4 

6X6 

ft 

109.44 

8955. 

81.8 

18.1 

8995. 

259 

3^ 

114.76 

9670. 

84.3 

260 

r£ 

119.96 

10365. 

86.4 

261 

1 

125.00 

11025. 

88.2 

18.2 

11090. 

49 


c 

FOUR  PLATES.        A-|j—  j-jj-B       FOUR   ANGLES. 

b 

Two  Web 

Two  Side 

FOUR  ANGLES 

'  Total 

AXIS  A.  B. 

Out  to  Out 

IV 

Plates, 

Plates, 

Area, 

of  Webs 

no. 

Size  in 

Size  in 

Size  in 

Thick- 

Square 

2 

for 

Inches 

Inches 

Inches 

ness 

Inches 

. 

Equal  I 

1 

18X# 

10^X3/8 

3^X3^ 

« 

38.88 

1392 

35.8 

11.3 

2 

% 

41.50 

1417 

34.1 

3 

;Hi 

H 

43.38 

1514 

34.9 

4 

46.00 

1538 

33.4 

5 

H 

/8 

51.55 

1739 

33.7 

11.0 

6 

18X3/ 

lO^XSxg 

3^X3^ 

H 

47.88 

1635 

34.1 

11.4 

7 

yt 

50.50 

1660 

32.9 

8 

% 

53.13 

1684 

31.7 

9 

^ 

50.80 

1812 

35.7 

10 

y* 

53.42 

1836 

34.4 

11 

N 

56.05 

1861 

33.2 

11.0 

12 

21X^ 

12^X3/8 

4X4 

M 

45.38 

2219 

48.9 

13.2 

13 

y* 

48.50 

2260 

46.6 

14 

3/1 

N 

48.82 

2506 

51.3, 

15 

y* 

51.94 

2546 

49.0 

16 

H 

55.07 

2587 

47.0 

12.8 

17 

21X# 

12%X3/& 

4X4 

M 

50.63 

2412 

*47.6 

13.2 

18 

l/t 

53.75 

2453 

45.6 

19 

f6 

56.88 

2493 

43.8 

20 

. 

N 

H 

54.07 

2699 

49.9 

21 

57.19 

2739 

47.9 

22 

# 

60.32 

2780 

46.1 

12.8 

23 

21X34 

12^X3/8 

4X4 

% 

55.88 

2605 

46.6 

13.3 

24 

y* 

59.00 

2646 

44.8 

25 

$ 

62.13 

2686 

43.2 

26 

^i 

65.25 

2727 

41.8 

27 

H 

H 

59.32 

2892 

48.8 

FOUR  PLATES.        FOUR  ANGLES. 

(CONTINUED.) 

Two  Web 

Two  Side 

FOUR  ANGLES 

Total 

AXIS  A.  B. 

Out  to  Out 

•ft 

Plates, 

Plates, 

Area, 

oHVeks 

HO. 

Size  in 

Size  in 

Size  in 

Thick- 

Square 

_2 

for 

Inches 

Inches 

Inches 

ness 

Inches 

r 

Equal  I 

28 

21X3^ 

12J*X# 

4X4 

ft 

62.44 

2932 

47.0 

29 

ft 

65.57 

2973 

45.3 

30 

68.69 

3014 

43.9 

12.6 

31 

21X^ 

I2y2xy2 

4X4 

ft 

67.69 

3125 

46.2 

13.1 

32 

ft 

70.82 

3166 

44.7 

33 

U 

73.94 

3206 

43.4 

34 

21X1 

i2y2xy2 

4X4 

y2 

69.50 

3032 

43.6 

35 

ft 

72.63 

3072 

42.3 

36 

l/2 

ft 

72.94 

3318 

45.5 

37 

ft 

76.07 

3359 

44.2 

13.0 

38 

24X^ 

i5y2x3/& 

4X4 

1A 

50.63 

3163 

62.5 

15.1 

39 

y2 

54.50 

3241 

59.5 

40 

ft 

ft 

61.82 

3706 

60.0 

41 

24X^j 

i5y2X3/z 

4X4 

l/2 

56.63 

3451 

60.9 

15.1 

42 

y* 

60.50 

3529 

58.3 

43 

ft 

64.38 

3606 

56.0 

44 

ft 

63.94 

3916 

61.2 

45 

ft 

67.82 

3994 

58.9 

14.7 

46 

24X3^ 

15%X3/z 

4X4 

Y2 

62.63 

3739 

59.7 

15.2 

47 

l/2 

66.50 

3817 

57.4 

43 

ft 

70.38 

3894 

55.3 

49 

ft 

66.07 

4126 

62.5 

50 

24x34; 

I5y2x% 

4X4 

ft 

69.94 

4204 

60.1 

51 

ft 

73.82 

4282 

58.0 

14.8 

52 

24XJ/S 

I5y2xy2 

4X4 

IA 

72.50 

4105 

56.6 

14.9 

53 

ft 

76.38 

4182 

54.8 

54 

ft 

75.94 

4492 

59.2 

c 

FOUR  PLATES.          A-Jj-  jj-B         FOUR  ANGLES. 

D 

Two  Web 

Two  Side 

FOUR  ANGLES 

Total 

AXIS  A.  B. 

Out  to  Out 

Plates, 

Plates. 

Area, 

of  Webs 

No. 

Size  in 
Inches 

Size  in 
Inches 

Size  in 
Inches 

Thtek- 
ness 

Square 
Inches 

I 

r2 

for 
Equal  I 

55 

24X    7/z 

i*X*X 

4X4 

X 

79.82 

4570 

57.3 

56 

k 

83.69 

4647 

55.5 

14.5 

57 

24X1 

15^X^ 

4X4 

X 

78.50 

4393 

56.0 

14.9 

58 

X 

82.38 

4470 

54.3 

59 

x 

81.94 

4780 

58.3 

60 

ft 

85.82 

4858 

56.6 

61 

I/ 

*/ 

85.26 

5150 

60.4 

62 

«£ 

89.14 

5228 

58.7 

63 

% 

93.01 

5305 

57.0 

14.8 

64 

24X1# 

15%X% 

4X4 

X 

93.94 

5356 

57.0 

65 

X 

97.82 

5434 

55.5 

66 

27X   ^ 

y* 

55.88 

4335 

77.6 

17.1 

67 

% 

60.50 

4467 

73.8 

68 

y* 

X 

59.32 

4839 

81.6 

69 

X 

63.94 

4971 

77.7 

16.9 

70 

27X   ft 

i8%xys 

4X4 

y* 

62.63 

4745 

75.8 

17  0 

71 

\/ 

67.25 

4877 

72.5 

72 

X 

X 

66.07 

5249 

79.4 

73 

% 

70.69 

5381 

76.1 

74 

X 

75.32 

5513 

73.2 

16.5 

75 

27X    |^ 

i8y2x% 

4X4 

X 

74.00 

5287 

71.4 

16.7 

76 

i^ 

77.44 

5791 

74.8 

77 

*<i 

82.07 

5923 

72.2 

78 

7/z 

/4 

X 

80.75 

5697 

70.5 

16.7 

79 

X 

88.82 

6333 

71.3 

80 

27X1 

18^X^ 

4X4 

x 

95.57 

6743 

70.6 

16.6 

81 

\K 

109.07 

7563 

69.3 

16  8 

52 


c 

B       I  BEAMS. 

p 

TWO  BEAMS 

ONE  BEAM 

Total 

No. 

Depth 
in  Ins. 

Lbs. 
per  Ft. 

Area  in 
Sq.  Ins. 

Depth  in 
Inches 

Lbs. 

per  Ft. 

Area  in 
Sq.  Ins. 

Area, 
Sq.  Ins. 

I 

r2 

l 

9 

21.0 

12.62 

7 

15.0 

4.42 

17.04 

172.5 

10  12 

2 

8 

18.0 

5.33 

17.95 

173.6 

9.67 

3 

9 

21.0 

6.31 

18.93 

175.0 

9.25 

'4 

10 

25.0 

7.37 

19.99 

176.7 

8.84 

5 

10 

25.0 

14.74 

8 

18.0 

5.33 

20.07 

248.0 

12.36 

6 

, 

9 

21.0 

6.31 

21.05 

249.4 

11.85 

7 

10 

25.0 

7.37 

22.11 

251.1 

11.36 

8 

12 

31.5 

9.26 

24.00 

253.7 

10.57 

9 

12 

31.5 

18.52 

9 

21.0 

6.31 

24.83 

436.8 

17.59 

10 

10 

25.0 

7.37 

25.89 

438.5 

16.94 

11 

12 

31.5 

9.26 

27.78 

441.1 

15.88 

12 

15 

42.0 

12.48 

31.00 

446.2 

14.39 

13 

15 

42.0 

24.96 

9 

21.0 

6.31 

31.27 

637.5 

20.39 

14 

10 

25.0 

7.37 

32.33 

798.4 

24.70 

15 

12 

31.5 

9.26 

34.22 

892.9 

26.09 

16 

15 

42.0 

12.48 

37.44 

898.0 

23.98 

17 

18 

55.0 

31.86 

10 

25.0 

7.37 

39.23 

993.5* 

25.33* 

18 

12 

31.5 

9.26 

41.12 

1452.  * 

35.31* 

19 

15 

42.0 

12.48 

44.34 

1606. 

36.22 

20 

18 

55.0 

15.93 

47.79 

1612. 

33.73 

21 

20 

65.0 

38.16 

12 

31.5 

9.26 

47.42 

1706.  * 

35.97* 

22 

15 

42.0 

12.48 

50.64 

2354. 

46.49 

23 

18 

55.0 

15.93 

54.09 

2360. 

43.64 

24 

20 

65.0 

19.08 

57.24 

2367. 

41.36 

25 

24 

80.0 

46.64 

12 

31.5 

9.26 

55.90 

2038.  * 

36.46* 

26 

15 

42.0 

12.48 

59.  *2 

3243.   * 

54.86* 

27 

18 

55.0 

15.93 

62.57 

4197. 

67.08 

28 

20 

65.0 

19.08 

65.72 

4204. 

63.98 

29 

24 

80.0 

23.32 

69.96 

4219. 

60.31 

*  These  values  are  about  Axis  C.  D.  ;  all  others  are  about  Axis  A.  B. 

53 


TWO  CHANNELS   A--|L»4—  4|      B   ONE  X  BEAM. 

11       •       •• 

J     6    L 

TWO  CHANNELS 

ONE  X  BEAM 

Total 

AXIS  A.  B. 

AXIS  C.  D. 

Area. 

No. 

Depth  in 
Inches 

Lbs.  pei- 
Foot 

Depth  in 
Inches 

Lbs.  pei- 
Foot 

Square 
Inches 

I 

r2 

I 

r2 

1 

6 

8.0 

4 

7.5 

6.97 

26.8 

3.84 

37.6 

5.40 

2 

5 

9.75 

7.63 

27.2 

3.57 

56.8 

7.44 

3 

6 

12.25 

8.37 

27.9 

3.33 

82.1 

9.81 

4 

7 

15.0 

9.18 

28.7 

3.12 

114.4 

12.5. 

5 

8 

18.0 

10.09 

29.8 

2.95 

155.4 

15.4 

6 

6 

15.5 

4 

7.5 

11.33 

39.8 

3.51 

67.7 

5.98 

7 

5 

9.75 

11.99 

40.2 

3.36 

99.3 

8.28 

8 

6 

12.25 

12.73 

40.9 

3.21 

139.0 

10.9 

9 

7 

15.0 

13  54 

41.7 

3.08 

188.1 

13.9 

10 

8 

18.0 

14.45 

42.8 

2.96 

247.9 

17.2 

11 

7 

9.75 

5 

9,75 

8.57 

43.4 

5.07 

66.9 

7.81 

12 

6 

12.25 

9.31 

44.1 

4.73 

95.4 

10.2 

13 

7 

15.0 

10.12 

44.9 

4.43 

131.5 

13.0 

14 

8 

18.0 

11.03 

46.0 

4.17 

176.6 

16.0 

15 

9 

21.0 

12.01 

47  4 

3.94 

232.0 

19.3 

16 

7 

12.25 

5 

9.75 

'10.07 

49.6 

4.93 

80.5 

7.99 

17 

6 

12.25 

10.81 

50.3 

4.65 

113.8 

10.5 

18 

7 

15.0 

11.62 

51.1 

4.39 

155.4 

13.4 

19 

8 

18.0 

12.53 

52.2 

4.16 

206.9 

16.5 

20 

9 

21.0 

13.51 

53.6 

3.96 

269.3 

19.9 

21 

7 

14.75 

5 

9.75 

11.55 

55.6 

4.82 

94.9 

8.22 

22 

6 

12.25 

12.29 

56.3 

4.58 

133.1 

10.8 

23 

7 

15.0 

13.10 

57.1 

4.36 

180.3 

13.8 

24 

8 

18.0 

14.01 

58.2 

4.15 

238.2 

17.0 

25 

9 

21.0 

14.99 

59.6 

3.97 

307.8 

20.5 

26 

7 

19.75 

5 

9.75 

14.49 

67.6 

4.67 

126.2 

8.71 

27 

6 

12.25 

15.23 

68.3 

4.48 

174.7 

11.5 

28 

7 

15.0 

16.04 

69.1 

4.31 

233.6 

14.6 

29 

8 

18.0 

16.95 

70.2 

4.14 

304.7 

18.0 

30 

9 

21.0 

17.93 

71.6 

3.99 

388-8 

21.7 

TWO   CHANNELS.       ONE  X  BEAM. 

(CONTINUED.) 

No. 

TWO  CHANNELS 

ONE  Z  BEAM 

Total 
Area, 
Square 
Inches 

AXIS  A.  B. 

AXIS  C.  D. 

Depth  in 
Inches 

Lk  per 
Foot 

Depth  in 
Inches 

Lbs.  per 

Foot 

I 

r2 

I 

r2 

31 

8 

11.25 

6 

12.25 

10.31 

66.5 

6.45 

110.1 

10.7 

32 

7 

15.0 

11.12 

67.3 

6.05 

150.2 

13.5 

33 

8 

18.0 

12.03 

68.4 

5.68 

199.9 

16.6 

34 

9 

21.0 

13.01 

69.8 

5.36 

260.2 

20.0 

35 

10 

25.0 

14.07 

71.5 

5.08 

333.1 

23  7 

36 

8 

13.75 

6 

12.25 

11.69 

73.9 

6.32 

127.1 

10-9 

37 

7 

15.0 

12.50 

74.7 

5.97 

172.3 

13.8 

38 

8 

18.0 

13.41 

75.8 

•5.65 

227.8 

17.0 

39 

9 

21.0 

14.39 

77.2 

5.36 

294.7 

20.5 

40 

10 

25.0 

15.45 

78.9 

5.11 

374.7 

24.3 

41 

8 

16.25 

6 

12.25 

13.17 

81.7 

6.20 

146.2 

11.1 

42 

7 

15.0 

13.98 

82.5 

5.90 

197.0 

14.1 

43 

8 

18.0 

14.89 

83.6 

5.61 

258.9 

17.4 

44 

9 

21.0 

15.87 

85.0 

5.35 

332.9 

21.0 

45 

10 

25.0 

16.93 

86.7 

5.12 

420.8 

24.9 

46 

8 

21.25 

6 

12.25 

16.11 

97.5 

6.05 

187.1 

11.6 

47 

7 

15.0 

16.92 

98.3 

5.81 

249.5 

14.7 

48 

8 

18.0 

17.83 

99  4 

5.57 

324.4 

18.2 

49 

9 

21.0 

18.81 

100.8 

5.36 

412.9 

22.0 

50 

10 

25.0 

19.67 

102.5 

5.16 

516.8 

26.0 

51 

9 

13.25 

6 

12.25 

11.39 

96.5 

8.47 

126.6 

11.1 

52 

7 

15.0 

12.20 

97.3 

7.97 

171.0 

14.0 

53 

8 

18.0 

13.11 

98.4 

7.50 

225.6 

17.2 

54 

9 

21.0 

14.09 

99.8 

7.08 

291.4 

20.7 

55 

10 

25.0 

15.15 

101.5 

6.70 

370.2 

24.4 

56 

9 

15.0 

6 

12.25 

12.43 

103.7 

8.34 

139.4 

11.2 

57 

7 

15.0 

13.24 

104.5 

7.89 

187.7 

14.2 

58 

8 

18.0 

14.15 

105.6 

7  46 

246.6 

17.4 

59 

9 

21.0 

15.13 

1.07.0 

7.07 

317.3 

21.0 

60 

10 

25.0 

16.19 

108.7 

£.71 

401.6 

24.8 

55 


]?  r 
L»*-Jl      3      ONE  Z  BEAM. 

TWO  CHANNELS 

ONE  I  BEAM 

Total 

AXIS  A.  B. 

AXIS  C.  D. 

No. 

Area, 
Square 
Inches 

Depth  iu 
Inches 

Lbs.  per 
Foot 

Depth  in 
Inches 

Lbs.  per 
Foot 

I 

r2 

I 

r2 

61 

9 

25.0 

6 

12.25 

18.31 

143.3 

7.82 

219.8 

12.0 

62 

7 

15.0 

19.12 

144.1 

7.54 

291.1 

15.2 

63 

8 

18.0 

20.03 

145.2 

7.25 

375.9 

18.8 

64 

9 

21.0 

21.01 

146.6 

6.98 

475.5 

22.6 

65 

10 

25.0 

22.07 

148.3 

6.72 

591.5 

26  8 

66 

10 

15.0 

6 

12.25 

12.53 

135.7 

10.8 

144.5 

11.5 

67 

7 

15.0 

13.34 

136.5 

10.2 

193.6 

14.5 

68 

8 

18.0 

14.25 

137.6 

9.65 

253.5 

17.8 

69 

9 

21.0 

15.23 

139.0 

9.12 

325.1 

21.3 

70 

10 

25.0 

16.29 

140.7 

8.64 

410.3 

25.2 

71 

10 

20.0 

6 

12-25 

15  37 

159.3 

10.4 

180.7 

11.8 

72 

7 

15.0 

16.18 

160.1 

9.89 

240.5 

14.9 

73 

8 

18.0 

17.09 

161.2 

9.43 

312.4 

18.3 

74 

9 

21.0 

18.07 

162.6 

9.00 

397.6 

22.0 

75 

10 

25.0 

19.13 

164.3 

8.59 

497.8 

26.0 

76 

10 

35.0 

6 

12.25 

24.19 

232.9 

9.63 

312.1 

12.9 

77 

7 

15.0 

25.00 

233.7 

9.35 

407.7 

16.3 

78 

8 

18.0 

25.91 

234.8 

9.06 

519.9 

20.1 

79 

9 

21.0 

26.89 

236.2 

8.78 

649.7 

24.2 

80 

10 

25.0 

27.95 

237.9 

8.51 

798.9 

28.6 

81 

12 

20.5 

7 

15.0 

16.48 

25a.9 

15.7 

257.2 

15.6 

82 

8 

18.0 

17.39 

260.0 

15.0 

331.6 

19.1 

83 

9 

21.0 

13.37 

261.4 

14.2 

419.3 

22.3 

84 

10 

25.0 

19.43 

263.1 

13.5 

522.3 

26.9 

85 

12 

31.5 

21.32 

265.7 

12.5 

765.7 

35.9 

86 

12 

25.0 

7 

15.0 

19.12 

290.7 

15.2 

301.9 

15.8 

87 

8          18.0 

20.03 

291.8 

14.6 

387.7 

19.4 

88 

9 

21.0 

21.01 

293.2 

14.0 

488.1 

23.2 

89 

10 

25.0 

22.07 

294.9 

13.4 

605.1 

27.4 

90 

• 

12 

31.5 

23.96 

297.5 

12.4 

880.4 

36.8 

TWO  CHANNELS.      ONE  X  BEAM. 

(CONTINUED.) 

TWO  CHAPELS 

ONE  I  BEAM 

Total 
Area, 

AXIS  A.  B. 

AXIS  C.  D. 

No. 

Depth  in 
Inches 

Lk  per 
Foot 

Depth  in 
inches 

Lbs.  per 
Foot 

Square 
inches 

I 

r2 

I 

r2 

91 

12 

30.0 

7 

15.0 

22.06 

326.1 

14.8 

354.4 

16.1 

92 

8 

18.0 

22.97 

327.2 

14.2 

453.2 

19.7 

93 

9 

21.0 

23.95 

328.6 

13.7 

568.1 

23.7 

94 

10 

25.0 

25.01 

330.3 

13.2 

701.1 

28.0 

95 

12 

31.5 

26.90 

332.9 

12.4 

1013. 

37.6 

96 

12 

35.0 

8 

18.0 

25.91 

362.4 

14.0 

522.1 

20.2 

97 

9 

21.0 

26.89 

363.8 

13.5 

651.9 

24.2 

98 

10 

25.0 

27.95 

365.5 

13.1 

801.1 

28.7 

99 

12 

31.5 

29.84 

368.1 

12.3 

1150. 

38.5 

100 

15 

42.0 

33.06 

373.2 

11.3 

1835. 

55.5 

101 

15 

33.0 

8 

18.0 

25.13 

629.0 

25.0 

528.4 

21.0 

102 

9 

21.0 

26.11 

630.4 

24.1 

656.3 

25.1 

103 

10 

25.0 

27.17 

632.1 

23.3 

803.2 

29.6 

104 

12 

31.5 

29.06 

634.7 

21.8 

1146. 

39.4 

105 

15 

42.0 

32.28 

639.8 

19.8 

1820. 

56.4 

106 

15 

35.0 

8 

18.0 

25.91 

643.8 

24.9 

545.9 

21.1 

107 

9 

21.0 

26.89 

645.2 

24.0 

677.6 

25.2 

108 

10 

25.0 

27.95 

646.9 

23.1 

828.7 

29.6 

109 

12 

31.5 

29.84 

649.5 

21.8 

1181. 

39.6 

110 

15 

42.0 

33.06 

654.6 

19.8 

1873. 

56.6 

111 

15 

40.0 

8 

18.0 

28.85 

698.8 

24.2 

613.8 

21.3 

112 

9 

21.0 

29.83 

700.2 

23.5 

760.1 

25.5 

113 

10 

25.0 

30.89 

701.9 

22.7 

927.4 

30.0 

114 

12 

31.5 

32.78 

704.5 

21.5 

1317. 

40.2 

115 

15 

42.0 

36.00 

709.6 

19.7 

2074. 

57.6 

116 

15 

55.0 

8 

18.0 

37.69 

864.2 

22.9 

834.0 

22  1 

117 

9 

21.0 

38.67 

865.6 

22.4 

1026. 

26.5 

118 

10 

25.0 

39.73 

867.3 

21.8 

1244. 

31.3 

119 

12 

31.5 

41.62 

869.9 

20.9 

1747. 

42.0 

120 

15 

42.0 

44.84 

875.0 

19.5 

2708. 

60.4 

57 


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210.4 

25 

8 

11.25 

5.0 

10x14: 

•    9.20 

1.12 

95.6 

10.4 

86.9 

26 

7.0 

13X34: 

9.70 

1.28 

100.0 

10.3 

150.0 

27 

13.75 

5.0 

iox  14: 

10.58 

0.97 

104.5 

9.88 

99.4 

28 

7.0 

12x^4: 

11.08 

1.12 

109.2 

9.86 

172.1 

29 

16.25 

5.0 

lOXyV 

12.69 

1.03 

120.6 

9.50 

118.9 

30 

7.0 

12XT56' 

13.31 

1.17 

126.4 

9.49 

205,8 

31 

18.75 

4.5 

10X3^ 

14.77 

1.06 

136.7 

9.26 

122.7 

32 

6.5 

12X^ 

15.52 

1.21 

143.7 

9.26 

218.6 

33 

21.25 

4.5 

lOxS/e' 

16.25 

0.97 

146.2 

9.00 

136.4 

34 

6.5 

12X3/8 

17.00 

1.11 

153.7 

9.04 

242.6 

75 


TWO  CHANNELS.       ONE  PLATE. 

(CONTINUED.) 

No. 

TWO  CHANNELS 

Dist, 
b.tob. 

Top 
Plato, 
Size  in 
Inches 

Total 
Area, 
Square 
Inches 

Eccen- 
tricity 

AXIS  A.  B. 

AXIS 

e.  D. 
i 

Depth  in 
Inches 

Lbs.  per 
Fool 

I 

r2 

35 

9 

13.25 

7.0 

12XX 

10.78 

1.29 

140.9 

13.1 

170.8 

36 

9.0 

14X% 

11.28 

1.44 

146.3 

13.0 

263.6 

37 

15.0 

7.0 

12x14: 

11.82 

1.17 

149.7 

12-7 

187.5 

38 

9.0 

14XX 

12.32 

1.31 

155.4 

12.6 

289.6 

39 

20.0 

6.5 

15.51 

1.13 

183.3 

11.8 

222.9 

40 

8.5 

14XT5r 

16.14 

1.26 

190.8 

11.8 

351.3 

41 

25.0 

6.0 

12X3/6 

19.20 

1.10 

217.2 

11.3 

252.1 

42 

8.0 

14X^-6 

19.95 

1.23 

226.5 

11.4 

404.8 

43 

10 

15.0 

6.5 

12Xi^ 

11.92 

1.29 

192.8 

16.2 

175.5 

44 

8.5 

14XX 

12.42 

1.44 

199.8 

16  1 

275.0 

45 

20.0 

6.5 

12XT5^ 

15.51 

1.25 

233.0 

15.0 

225.8 

46 

8.5 

14  X  5 

16.14 

1.40 

242.3 

15.0 

354.8 

47 

10.5 

16XT5^ 

16.76 

1.54 

250.7 

15.0 

516.1 

48 

25.0 

6.0 

12X^| 

19.20 

1.22 

274.8 

14.3 

253.4 

49 

8.0 

14X^8 

19.95 

1.37 

286.2 

14.4 

406.3 

50 

10.0 

lex^g" 

20.70 

1.50 

296.8 

14.3 

599.1 

51 

12 

20.5 

8.0 

14x14: 

15.56 

1.38 

358.0 

23.0 

331.9 

52 

25.0 

7.5 

14XX 

18.20 

1.18 

394.1 

21.7 

354.4 

53 

7.5 

14X-A- 

19.08 

1.41 

415.9 

21.8 

368.7 

54 

7.5 

14X^| 

19.95 

1-63 

436.2 

21.9 

383.0 

55 

9.5 

16X  ST 

19.70 

1.56 

429.4 

21.8 

548.8 

56 

9.5 

16X^| 

20.70 

1.79 

44*1.2 

21.3 

570.2 

57 

11.5 

18X^6 

21.45 

1.95 

465.2 

21.7 

798.5 

58 

30.0 

7.5 

14  XT\ 

22.02 

1.22 

456.4 

20.7 

427.6 

59 

7.5 

14X^ 

22.89 

1.42 

478.4 

20.9 

441.9 

60 

7.5 

14XT77r 

23.77 

1.60 

499.4 

21.0 

456.2 

61 

9.5 

16XT5<T 

22.64 

1.36 

471.1 

20.8 

636.6 

62 

9.5 

16X^6 

23.64 

1.57 

494.9 

20.9 

657.9 

63 

9.5 

16XT7^ 

24.64 

1.77 

517.3 

21.0 

679.3 

64 

11.5 

ISXa^ 

24.39 

1.71 

510.4 

20.9 

921.3 

65 

11.5 

l8xxV 

25.52 

1.92 

534.2 

20.9 

951.8 

66 

35.0 

7.0 

14*H 

25.83 

1.26 

518.8 

20.1 

469.6 

67 

7.0 

14XTS 

26.71 

1.43 

541.4 

20.3 

473.8 

68 

7.0 

14XJ£ 

27.58 

1.59 

562.8 

20.4 

488.1 

69 

9.0 

16X/8 

26.58 

1.40 

536.6 

20.2 

695.0 

70 

9.0 

27.58 

1.58 

560.7 

20.3 

716.3 

71 

9.0 

15x  y. 

28.58 

1.75 

583.8 

20.4 

737.7 

72 

11.0 

18X^/3 

27.33 

1.53 

553.3 

20.3 

983.6 

73 

11.0 

28.46 

1.72 

579.1 

20.4 

1014. 

74 

11.0 

18Xi| 

29.58 

1.90 

603.4 

20.4  1044. 

76 


C" 

TWO  CHANNELS       A-]—*  B       ONE  PLATE. 

J     D    L 

TWO  CHANNELS 

Top 

Total 

AXIS  A.  B. 

AXIS 

No. 

b.  to'b. 

Plate, 
Size  in 
Inches 

Area, 
Square 
Inches 

Eccen- 
tricity 

C.D. 
I 

Depth  in 
Inches 

Lbs.  per 
Foot 

I 

r2 

75 

15 

33.0 

9.0 

16XT\ 

24.80 

1.54 

859.2 

34.6 

678.0 

76 

9.0 

16X^8 

25.80 

1.79 

897.4 

34.8 

699.4 

77 

11.0 

18X3/8 

26.55 

1.96 

922.8 

34.8 

983.1 

78 

13.0 

20X3/£ 

27.30 

2.11 

946.8 

34.7 

1320. 

79 

35.0 

9.0 

16XA 

25.58 

1.50 

875.8 

34:2 

699.3 

80 

9.0 

16X3/8 

26.58 

1.74 

914.7 

34.4 

720.6 

81 

9.0 

16XT* 

27.58 

1.96 

951.3 

34.5 

741.9 

82 

11.0 

18X3/8 

27.33 

1.90 

940.5 

34.4 

1013. 

83 

11.0 

18X-^ 

28.46 

2.14 

979.7 

34.4 

1044. 

84 

13.0 

WXji 

28.08 

2.05 

965.0 

34.4 

1360. 

85 

13.0 

20xyV 

29.33 

2.30 

1006. 

34.3 

1402. 

86 

40.0 

8.5 

lexf/g- 

29.52 

1.56 

977.6 

33.1 

742.6 

87 

8.5 

lex^ 

30.52 

1.77 

1017. 

33.3 

763.9 

88 

8.5 

16X  l£ 

31.52 

1.97 

1054. 

33.4 

785.2 

89 

10.5 

18X3/£ 

30.27 

1.71 

1005. 

33.2 

1057. 

90 

10.5 

18X^ 

31.40 

1.94 

1047. 

33.3 

1087. 

91 

10.5 

32.52 

2.15 

1086. 

33.4 

1118. 

92 

12.5 

20X^/8 

31.02 

1.86 

1031. 

33.2 

1432. 

93 

12.5 

20  XX 

32.27 

2.09 

1075. 

33.3 

1474. 

94 

12.5 

20X^' 

33.52 

2.31 

1117. 

33.3 

1515. 

95 

45.0 

8.5 

16X|/8 

32.48 

1.42 

1039. 

32.0 

821.0 

96 

8.5 

33.48 

1.61 

1080. 

32.3 

842.0 

97 

8.5 

16XJ£ 

34.48 

1.80 

1119. 

32.5 

863.3 

98 

8.5 

16X5£ 

36.48 

2.14 

1194. 

32.7 

906.0 

99 

10.5 

18X3/8 

33.23 

1.56 

1068. 

32.2 

1168. 

100 

10.5 

34.36 

1.77 

1112. 

32.4 

1199. 

101 

10.5 

18XJ£ 

35.48 

1.97 

1154. 

32.5 

1229. 

102 

10.5 

18X^1 

37.73 

2.33 

1233. 

32.7 

1290. 

103 

12.5 

20X3/8 

33.98 

1.70 

1096. 

32.2 

1582. 

104 

12.5 

35.23 

1.92 

1142. 

32.4 

1624. 

105 

12.5 

2ox  y. 

36.48 

2.12 

1186. 

32.5 

1666. 

106 

12.5 

20X^ 

38.98 

2.51 

1269. 

32.6 

1749. 

107 

16.5 

24Xi^ 

38.48 

2.42 

1246. 

32.4 

2760. 

108 

16.5 

41.48 

2.83 

1335. 

32.2 

2904. 

77 


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eg 

5* 

x 

T-I 

CO 

•4) 

X 

OS 

'* 

X 

<M 

^ 

X 

03 
CM 

^ 

X 

OJ 
0) 

N^^       ^ 

X 

«*• 

CM 

**    10    CO 

t-  oo  o> 

0    .-I    CNJ    00    •<»- 

CM  <M  oa  csj  ca 

IO   CO   (V 
CM   CM   CM 

OO   CD   O 

CM    03    CD 

T-I  CM  oo  *»•  to 

85 


VALUES  OF  L-  L=L"""h  '"  Feel' 

r2  r-  Radius  of  Gyration  In  Inches. 

r2 

LENGTH  IN  FEET. 

in 

Inches 

8 

10 

12 

14 

15 

16 

18 

20 

22 

24 

26 

0.0 

0.1 

640 

1000 

1440 

1960 

0.2 

320 

500 

720 

980 

0.3 

213 

333 

480 

653 

750 

0.4 

160 

250 

360 

490 

562 

640 

0,5 

128 

200 

288 

392 

450 

512 

648 

0.6 

107 

167 

240 

327 

375 

427 

540 

667 

0.7 

91 

143 

206 

280 

321 

366 

463 

572 

692 

0.8 

80 

125 

180 

245 

281 

320 

405 

500 

605 

720 

0.9 

71 

111 

160 

218 

250 

284 

360 

444 

538 

640 

751 

1.0 

64 

100 

144 

196 

225 

256 

324 

400 

484 

576 

676 

1.1 

58 

91 

131 

178 

205 

233 

295 

364 

440 

524 

615 

1.2 

53 

83 

120 

163 

187 

213 

270 

333 

403 

480 

563 

1.3 

49 

77 

111 

151 

173 

197 

249 

308 

372 

443 

520 

1.4 

46 

71 

103 

140 

161 

183 

231 

286 

346 

411 

483 

1.5 

43 

67 

96 

131 

150 

171 

216 

267 

323 

384 

451 

1.6 

40 

62 

90 

122 

141 

160 

202 

250 

302 

360 

422 

1.7 

38 

59 

85 

115 

132 

151 

191 

235 

285 

339 

398 

1.8 

36 

56 

80 

109 

125 

142 

180 

222 

269 

320 

376 

1.9 

34 

53 

76 

103 

118 

135 

171 

211 

255 

303 

356 

2.0 

32 

50 

72 

98 

112 

128 

162 

200 

242 

288 

338 

2.1 

30 

48 

69 

93 

107 

122 

154 

191 

231 

274 

322 

2.2 

29 

45 

65 

89 

102 

116 

147 

182 

220 

262 

307 

2.3 

28 

43 

63 

85 

98 

112 

141 

174 

210 

250 

294 

2.4 

27 

42 

60 

82 

94 

107 

135 

167 

202 

240 

282 

2.5 

26 

40 

58 

78 

90 

102 

130 

160 

194 

230 

270 

2.6 

25 

38 

55 

75 

87 

98 

125 

154 

186 

222 

260 

2.7 

24 

37 

53 

73 

83 

95 

120 

148 

179 

213 

250 

2.8 

23 

36 

51 

70 

80 

91 

116 

143 

173 

206 

241 

2.9 

22 

"34 

50 

68 

0 

78 

88 

112 

138 

167 

199 

233 

3.0 

21 

33 

48 

65 

75 

85 

108 

133 

161 

192 

225 

3.1 

21 

32 

46 

63 

73 

83 

105 

129 

156 

186 

218 

3.2 

20 

31 

45 

61 

70 

80 

101 

125 

151 

180 

211 

3.3 

19 

30 

44 

59 

68 

78 

98 

121 

147 

175 

205 

3.4 

19 

29 

42 

58 

66 

75 

95 

118 

142 

169 

199 

3.5 

18 

29 

41 

56 

64 

73 

93 

114 

138 

165 

193 

3.6 

18 

28 

40 

54 

62 

71 

90 

111 

134 

160 

188 

3.7 

17 

27 

39 

53 

61 

69 

88 

108 

131 

156 

183 

3.8 

17 

26 

38 

52 

59 

67 

85 

105 

127 

152 

178 

3.9 

16 

26 

37 

50 

58 

66 

83 

103 

124 

148 

173 

4.0 

16 

25 

36 

49 

56 

64 

81 

100 

121 

144 

169 

4.1 

16 

24 

35 

48 

55 

62 

79 

98 

118 

141 

165 

4.2 

15 

24 

34 

47 

54 

61 

77 

95 

115 

137 

161 

4.3 

15 

23 

34 

46 

52 

60 

75 

93 

113 

134 

157 

4.4 

15 

23 

33 

45 

51 

58 

74 

91 

110 

131 

154 

VALUES  OF  ^  •-*"««"•**. 

r2  r-  Radius  of  Gyration  in  Inches. 

LENGTH  IN  FEET 

r2 
in 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

Inches 

0.0 

0.1 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

784 

10 

713 

818 

1.1 

653 

750 

853 

1.2 

603 

692 

788 

889 

1.3 

560 

643 

731 

826 

926 

1.4 

523 

600 

683 

771 

864 

963 

1.5 

490 

562 

640 

723 

810 

903 

1.6 

461 

529 

602 

680 

762 

849 

S41 

U7 

436 

500 

569 

642 

720 

802 

889 

980 

1.8 

413 

474 

539 

608 

682 

760 

842 

928 

1.9 

392 

450 

512 

578 

648 

722 

800 

882 

968 

20 

373 

429 

488 

551 

617 

688 

762 

840 

922 

2.1 

356 

409 

466 

526 

589 

656 

727 

802 

880 

962 

2.2 

341 

391 

445 

503 

564 

628 

696 

767 

842 

920 

2.3 

327 

375 

427 

482 

540 

602 

667 

735 

807 

882 

960 

2.4 

314 

360 

410 

462 

518 

578 

640 

706 

774 

846 

922 

2.5 

302 

346 

394 

445 

498 

555 

615 

678 

745 

814 

886 

962 

2.6 

290 

333 

379 

428 

480 

535 

593 

653 

717 

784 

853 

926 

2.7 

280 

321 

366 

413 

463 

516 

571 

630 

691 

756 

823 

893 

2.8 

270 

310 

353 

399 

447 

498 

552 

608 

668 

730 

795 

862 

2.9 

261 

300 

341 

385 

432 

481 

533 

588 

645 

705 

768 

833 

3.0 

253 

290 

330 

373 

418 

466 

516 

569 

625 

683 

743 

806 

3.1 

245 

281 

320 

361 

405 

451 

500 

551 

605 

661 

720 

781 

3.2 

238 

273 

310 

350 

393 

438 

485 

535 

587 

641 

698 

758 

3.3 

231 

265 

301 

340 

381 

425 

471 

519 

569 

622 

678 

735 

3.4 

224 

257 

293 

330 

370 

413 

457 

504 

•553 

605 

658 

714 

3.5 

218 

250 

284 

321 

360 

401 

444 

490 

538 

588 

640 

695 

3.6 

212 

243 

277 

312 

350 

390 

433 

477 

523 

572 

623 

676 

3.7 

206 

237 

269 

404 

341 

380 

421 

464 

509 

557 

606 

658 

3.8 

201 

231 

263 

296 

332 

370 

410 

452 

496 

543 

591 

641 

3.9 

196 

225 

256 

289 

324 

361 

400 

441 

484 

529 

576 

625 

40 

191 

220 

250 

282 

316 

352 

390 

430 

472 

516 

562 

610 

4.1 

187 

214 

244 

275 

309 

344 

381 

420 

461 

504 

549 

595 

4.2 

182 

209 

238 

269 

301 

336 

372 

410 

450 

492 

536 

581 

4.3 

178 

205 

233 

263 

295 

328 

364 

401 

440 

481 

524 

568 

4.4 

p 

VALUES  OF  — 

r2  r=Radius  of  Gyration  in  Inches. 

r2 

LENGTH  IN  FEET. 

in 

Inches 

8 

10 

12 

14 

15 

16 

18 

20 

22 

24 

26 

45 

14 

22 

32 

44 

50 

57 

72 

89 

108 

128 

150 

4.6 

14 

22 

31 

43 

49 

56 

70 

87 

105 

125 

147 

4.7 

14 

21 

31 

42 

48 

55 

69 

85 

103 

123 

144 

4'.8 

13 

21 

30 

41 

47 

53 

67 

83 

101 

120 

141 

4.9 

13 

20 

29 

40 

46 

52 

66 

82 

99 

118 

133 

5.0 

13 

20 

29 

39 

45 

51 

65 

80 

97 

115 

135 

5  1 

13 

20 

28 

33 

44 

50 

64 

78 

95 

113 

133 

5.2 

12 

19 

28 

38 

43 

49 

62 

77 

93 

111 

130 

5.3 

12 

19 

27 

37 

42 

48 

61 

75 

.91 

109 

128 

5.4 

12 

19 

27 

36 

42 

47 

60 

74 

90 

107 

125 

5.5 

12 

18 

26 

36 

41 

47 

59 

73 

88 

105 

123 

5.6 

11 

18 

26 

35 

40 

46 

58 

71 

86 

103 

121 

5.7 

11 

18 

25 

34 

39 

45 

57 

70 

85 

101 

119 

5.8 

11 

17 

25 

34 

39 

44 

56 

69 

83 

99 

117 

5.9 

11 

17 

24 

33 

38 

43 

55 

68 

82 

98 

115 

6.0 

11 

17 

24 

33 

37 

43 

54 

67 

81 

96 

113 

6.1 

10 

16 

24 

32 

37 

42 

53 

66 

79 

94 

111 

6.2 

10 

16 

23 

32 

36 

41 

52 

65 

78 

93 

109 

6.3 

10 

16 

23 

31 

36 

41 

51 

63 

77 

91 

107 

64 

10 

16 

23 

31 

35 

40 

51 

62 

76 

90 

106 

6.5 

10 

15 

22 

30 

35 

39 

50 

62 

74 

89 

104 

6.6 

10 

15 

22 

30 

34 

39 

49 

61 

73 

87 

102 

6.7 

10 

15 

21 

29 

34 

38 

48 

60 

72 

86 

101 

6.8 

9 

15 

21 

29 

33 

38 

48 

59 

71 

85 

99 

6.9 

9 

14 

21 

28 

33 

37 

47 

58 

70 

83 

98 

7.0 

9 

14 

21 

28 

32 

37 

46 

57 

69 

82 

97 

7.1 

9 

14 

20 

28 

32 

36 

46 

56 

68 

81 

95 

7.2 

9 

14 

20 

27 

31 

36 

45 

56 

67 

80 

94 

7.3 

9 

14 

20 

27 

31 

35 

44 

55 

66 

79 

93 

7.4 

9 

14 

19 

26 

30 

35 

44 

54 

65 

78 

91 

7.5 

9 

13 

19 

26 

30 

34 

43 

53 

65 

77 

90 

7.6 

8 

13 

19 

26 

30 

34 

43 

53 

64 

76 

89 

7.7 

8 

13 

19 

25 

29 

33 

42 

52 

63 

75 

83 

7.8 

8 

13 

13 

25 

29 

33 

42 

51 

62 

74 

87 

7.9 

8 

13 

18 

25 

28 

32 

41 

51 

61 

73 

86 

8.0 

8 

12 

13 

25 

28 

32 

41 

50 

61 

72 

85 

8.1 

8 

12 

18 

24 

28 

32 

40 

49 

60 

71 

83 

8.2 

8 

12 

18 

24 

27 

31 

40 

49 

59 

70 

82 

8.3 

8 

12 

17 

24 

27 

31 

39 

48 

58 

69 

81 

8.4 

8 

12 

17 

23 

27 

30 

39 

48 

58 

69 

80 

8.5 

8 

12 

17 

23 

26 

30 

38 

47 

57 

68 

80 

86 

7 

12 

17 

23 

26 

30 

33 

47 

56 

67 

79 

8.7 

7 

11 

17 

23 

26 

29 

37 

46 

56 

66 

78 

8.8 

7 

11 

16 

22 

26 

29 

37 

45 

55 

65 

77 

8.9 

7 

11 

16 

22 

25 

29 

36 

45 

54 

65 

76 

L2  L=Length  in  Feet. 
VALUES  OF- 

r-   r  Radius  of  Gyration  in  Inches. 

LENGTH  IN  FEET 

r2 

in 

28 

30 

32 

34 

36 

38 

40 

42 

44 

'46 

48 

50 

Inches 

174 

200 

228 

257 

288 

321 

356 

392 

430 

470 

512 

556 

4.5 

170 

196 

223 

251 

282 

314 

348 

384 

421 

460 

501 

544 

4.8 

167 

192 

218 

246 

276 

307 

340 

375 

412 

450 

490 

532 

4.7 

163 

188 

213 

241 

270 

301 

333 

363 

403 

441 

480 

521 

4  8 

160 

184 

209 

236 

265 

295 

327 

360 

395 

432 

470 

510 

4.9 

157 

180 

205 

231 

259 

289 

320 

353 

387 

423 

461 

500 

50 

154 

176 

201 

227 

254 

283 

314 

346 

380 

415 

452 

490 

5.1 

151 

173 

197 

222 

249 

278 

308 

339 

372 

407 

443 

481 

5.2 

148 

170 

193 

218 

245 

273 

302 

333 

365 

399 

435 

472 

53 

145 

167 

190 

214 

240 

267 

296 

327 

359 

392 

427 

463 

5.4 

143 

164 

186 

210 

236 

263 

291 

321 

352 

385 

419 

455 

5.5 

140 

161 

183 

206 

231 

253 

286 

315 

346 

378 

411 

446 

56 

138 

158 

180 

203 

227 

253 

281 

309 

340 

371 

404 

439 

5.7 

135 

155 

177 

199 

223 

249 

276 

304 

334 

365 

397 

431 

5.8 

133 

153 

174 

196 

220 

245 

271 

299 

328 

359 

391 

424 

59 

131 

150 

171 

193 

216 

241 

267 

294 

323 

353 

384 

417 

60 

129 

148 

168 

190 

212 

237 

262 

289 

317 

347 

378 

410 

6.1 

126 

145 

165 

186 

209 

233 

258 

285 

312 

341 

372 

403 

6.2 

124 

143 

163 

184 

206 

229 

254 

280 

307 

336 

366 

397 

6.3 

123 

141 

160 

181 

203 

226 

250 

276 

303 

331 

360 

391 

6.4 

121 

138 

158 

178 

199 

222 

246 

271 

298 

326 

355 

385 

6.5 

119 

136 

155 

175 

196 

219 

242 

267 

293 

321 

349 

379 

6.6 

117 

134 

153 

173 

193 

216 

239 

263 

289 

316 

344 

373 

6.7 

115 

132 

151 

170 

191 

212 

235 

259 

285 

311 

339 

368 

6.8 

114 

130 

148 

168 

188 

209 

232 

256 

281 

307 

334 

362 

6.9 

112 

129 

146 

165 

185 

206 

229 

252 

277 

302 

329 

357 

7.0 

110 

127 

144 

163 

183 

203 

225 

248 

273 

298 

325 

352 

7.1 

109 

125 

142 

161 

180 

201 

222 

245 

269 

294 

320 

347 

7.2 

107 

123 

140 

158 

178 

198 

219 

242 

265 

290 

316 

342 

7.3 

106 

122 

138 

156 

175 

195 

216 

238 

262 

286 

311 

338 

7.4 

105 

120 

137 

154 

173 

193 

213 

235 

258 

282 

307 

333 

7.5 

103 

118 

135 

152 

171 

190 

211 

232 

255 

278 

303 

329 

7.6 

102 

117 

133 

150 

168 

188 

208 

229 

251 

275 

299 

325 

7.7 

101 

115 

131 

148 

166 

185 

205 

226 

248 

271 

295- 

321 

7.8 

99 

114 

130 

146 

164 

183 

203 

223 

245 

268 

292 

316 

7.9 

98 

113 

128 

145 

162 

182 

200 

221 

242 

265 

288 

313 

80 

97 

111 

126 

143 

160 

178 

198 

218 

239 

261 

284 

309 

8  1 

96 

110 

125 

141 

158 

176 

195 

215 

236 

258 

281 

305 

8.2 

94 

108 

123 

139 

156 

174 

193 

213 

233 

255 

278 

301 

8.3 

93 

107 

122 

138 

154 

172 

191 

210 

230 

252 

274 

298 

8.4 

92 

106 

120 

136 

152 

170 

188 

208 

228 

249 

271 

294 

8  5 

91 

105 

119 

134 

151 

168 

186 

205 

225 

246 

268 

291 

8.6 

90 

103 

118 

133 

149 

166 

184 

203 

223 

243 

265 

287 

8.7 

89 

102 

116 

131 

147 

164 

182 

200 

220 

240 

262 

284 

8.8 

88 

101 

115 

130 

146 

162 

180 

198 

218 

238 

259 

281 

8.9 

89 


VALUES  OF  ±-'  1-1-9*  i-FW. 

r2  r--  Radius  of  Gyration  in  Inches. 

r2 
in 

LENGTH  IN  FEET. 

Inches 

8 

10 

12 

14 

15 

16 

18 

20 

22 

24 

2b 

9.0 

7 

11 

16 

22 

25 

28 

36 

44 

54 

64 

75 

9.1 

7 

11 

16 

22 

25 

28 

36 

44 

53 

63 

74 

9.2 

7 

11 

16 

21 

24 

28 

35 

43 

53 

63 

73 

9.3 

7 

11 

15 

21 

24 

28 

35 

43 

52 

62 

73 

9.4 

7 

11 

15 

21 

24 

27 

34 

43 

52 

61 

72 

9.5 

7 

11 

15 

21 

24 

27 

34 

42 

51 

61 

71 

9.6 

7 

10 

15 

20 

23 

27 

34 

42 

50 

60 

70 

9.7 

7 

10 

15 

20 

23 

26 

33 

41 

50 

59 

70 

9.8 

7 

10 

15 

20 

23 

26 

33 

41 

49 

59 

69 

9.9 

6 

10 

15 

20 

23 

26 

33 

40 

49 

58 

68 

10.0 

6 

10 

14 

20 

23 

26 

32 

40 

48 

58 

68 

10.1 

6 

10 

14 

19 

22 

25 

32 

40 

48 

57 

67 

10.2 

6 

10 

14 

19 

22 

25 

32 

39 

47 

56 

66 

10.3 

6 

10 

14 

19 

22 

25 

31 

39 

47 

56 

66 

10.4 

6 

10 

14 

19 

22 

25 

31 

38 

47 

55 

65 

10.5 

6 

10 

14 

19 

21 

24 

31 

38 

46 

55 

64 

10.6 

6 

9 

14 

18 

21 

24 

31 

38 

46 

54 

64 

10.7 

6 

9 

13 

18 

21 

24 

30 

37 

45 

54 

63 

10.8 

6 

9 

13 

18 

21 

24 

30 

37 

45 

53 

63 

10.9 

6 

9 

13 

18 

21 

23 

30 

37 

44 

53 

62 

11.0 

6 

9 

13 

18 

20 

23 

29 

36 

44 

52 

61 

11.1 

6 

9 

13 

18 

20 

23 

29 

36 

44 

52 

61 

11.2 

6 

9 

13 

18 

20 

23 

29 

36 

43 

51 

60 

11.3 

6 

9 

13 

17 

20 

23 

29 

35 

43 

51 

60 

11.4 

6 

9 

13 

17 

20 

22 

28 

35 

42 

51 

59 

11  5 

6 

9 

13 

17 

20 

22 

28 

35 

42 

50 

59 

11.6 

6 

9 

12 

17 

19 

22 

28 

34 

42 

50 

58 

11.7 

5 

9 

12 

17 

19 

22 

28 

34 

41 

49 

58 

11.8 

5 

8 

12 

17 

19 

22 

27 

34 

41 

49 

57 

11.9 

5 

8 

12 

16 

19 

22 

27 

34 

41 

48 

57 

12.0 

5 

8 

12 

16 

19 

21 

27 

33 

40 

48 

56 

12.5 

5 

8 

12 

16 

18 

20 

26 

32 

39 

46 

54 

13.0 

5 

8 

11 

15 

17 

20 

25 

31 

37 

44 

52 

13.5 

5 

7 

11 

15 

17 

19 

24 

30 

36 

43 

50 

14.0 

5 

7 

10 

14 

16 

18 

23 

29 

35 

41 

48 

14.5 

4 

7 

10 

14 

16 

,18 

22 

28 

33 

40 

47 

15.0 

4 

7 

10 

13 

15 

17 

22 

27 

32 

38 

45 

15.5 

4 

6 

9 

13 

15 

17 

21 

26 

31 

37 

44 

16.0 

4 

6 

9 

12 

14 

16 

20. 

25 

30 

36 

42 

16.5 

4 

6 

9 

12 

14 

16 

20 

24 

29 

35 

41 

17.0 

4 

6 

8 

12 

13 

15 

19 

24 

28 

34 

40 

17.5 

4 

6 

8 

11 

13 

15 

19 

23 

28 

33 

39 

18.0 

4 

6 

8 

11 

13 

14 

18 

22 

27 

32 

38 

18.5 

3 

5 

8 

11 

12 

14 

18 

22 

26 

31 

37 

19.0 

3 

5 

8 

10 

12 

13 

17 

21 

25 

30 

36 

L2  L—  Length  in  Feet. 
VALUES  OF  — 

r2  r=Radius  of  Gyration  in  Inches. 

LENGTH  IN  FEET 

r2 

in 

23 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

Inches 

87 

100 

114 

128 

144 

160 

178 

196 

215 

235 

256 

278 

9.0 

86 

99 

113 

127 

142 

159 

176 

194 

213 

233 

253 

275 

9.1 

85 

98 

111 

126 

141 

157 

174 

192 

210 

230 

250 

272 

92 

84 

97 

110 

124 

139 

155 

172 

190 

208 

228 

248 

269 

9.3 

83 

96 

109 

123 

138 

154 

170 

188 

206 

225 

245 

266 

9.4 

83 

95 

108 

122 

136 

152 

168 

186 

204 

223 

243 

263 

9.5 

82 

94 

107 

120 

135 

150 

167 

184 

202 

220 

240 

260 

9.6 

81 

93 

106 

119 

134 

149 

165 

182 

200 

218 

238 

258 

9.7 

80 

92 

104 

118 

132 

147 

163 

180 

198 

216 

235 

255 

9.8 

79 

91 

103 

117 

131 

146 

162 

178 

196 

214 

233 

253 

9.9 

78 

90 

102 

116 

130 

144 

160 

176 

194 

212 

230 

250 

10.0 

78 

89 

101 

114 

128 

143 

158 

175 

192 

210 

228 

248 

10.1 

77 

88 

100 

113 

127 

142 

157 

173 

190 

207 

226 

245 

10.2 

76 

87 

99 

112 

126 

140 

155 

171 

188 

205 

224 

243 

10.3 

75 

87 

98 

111 

125 

139 

154 

170 

186 

203 

222 

240 

10.4 

75 

86 

98 

110 

123 

138 

152 

168 

184 

202 

219 

238 

10.5 

74 

85 

97 

109 

122 

136 

151 

166 

183 

200 

217 

236 

10.6 

73 

84 

96 

108 

121 

135 

150 

165 

181 

198 

215 

234 

107 

73 

83 

95 

107 

120 

134 

148 

163 

179 

196 

213 

231 

10.8 

72 

83 

94 

106 

119 

132 

147 

162 

178 

194 

211 

229 

10.9 

71 

82 

93 

105 

118 

131 

145 

160 

176 

192 

209 

227 

11.0 

71 

Bl' 

92 

104 

Hi 

130 

144 

159 

174 

191 

208 

225 

11.1 

70 

80 

91 

103 

116 

129 

143 

157 

173 

189 

206 

223 

11.2 

69 

80 

91 

102 

115 

128 

142 

156 

171 

187 

204 

221 

11.3 

69 

79 

90 

101 

114 

127 

140 

155 

170 

186 

202 

219 

11.4 

68 

78 

89 

101 

113 

126 

139 

153 

168 

184 

200 

217 

11.5 

68 

78 

88 

100 

112 

124 

138 

152 

167 

182 

199 

216 

11.6 

67 

77 

88 

99 

111 

123 

137 

151 

165 

181 

197 

214 

11.7 

66 

76 

87 

98 

110 

122 

136 

149 

164 

179 

195 

212 

11.8 

66 

76 

86 

97 

109 

121 

134 

148 

163 

178 

194 

210 

11.9 

65 

75 

85 

96 

108 

120 

133 

147 

161 

176 

192 

208 

12.0 

63 

72 

82 

92 

104 

116 

128 

141 

155 

169 

184 

200 

12.5 

60 

69 

79 

89 

100 

111 

123 

136 

149 

163 

177 

192 

13.0 

58 

67 

76 

86 

96 

107 

119 

131 

143 

157 

171 

185 

13.5 

56 

64 

73 

83 

93 

103 

114 

126 

138 

151 

165 

179 

14.0 

54 

62 

71 

80 

89 

100 

110 

122 

134 

146 

159 

172 

14.5 

52 

60 

68 

77 

86 

96 

107 

118 

129 

141 

154 

167 

15.0 

51 

58 

66 

75 

84 

93 

103 

114 

125 

137 

149 

161 

15.5 

49 

56 

64 

72 

81 

90 

100 

110 

121 

132 

144 

156 

16.0 

48 

55 

62 

70 

79 

88 

97 

107 

117 

128 

140 

152 

165 

46 

53 

60 

68 

76 

85 

94 

104 

114 

124 

136 

147 

17.0 

45 

51 

59 

66 

74 

83 

91 

101 

111 

121 

132 

143 

17.5 

44 

50 

57 

64 

72 

80 

89 

98 

108 

118 

128 

139 

18.0 

42 

49 

55 

62 

70 

78 

86 

95 

105 

114 

125 

135 

18.5 

41 

47 

54 

61 

68 

76 

84 

93 

102 

111 

121 

132 

19.0 

VALUES  OF^!    "-=l..n,thinFee,. 

r2    r=Radius  of  Gyration  in  Inches. 

r2 

LENGTH  IN  FEET. 

in 

Inches 

8 

10 

12 

14 

15 

16 

18 

20 

22 

24 

26 

19.5 

3 

5 

7 

10 

12 

13 

17 

21 

25 

30 

35 

20.0 

3 

5 

7 

10 

11 

13 

16 

20 

24 

29 

34 

20.5 

3 

5 

7 

10 

11 

12 

16 

20 

24 

28 

33 

21.0 

3 

5 

7 

9 

11 

12 

15 

19 

23 

27 

32 

21.5 

3 

5 

7 

9 

10 

12 

15 

19 

23 

27 

31 

22.0 

3 

5 

V 

9 

10 

12 

15 

18 

22 

26 

31 

22.5 

3 

4 

6 

9 

10 

11 

14 

18 

22 

26 

30 

23.0 

3 

4 

6 

9 

10 

11 

14 

17 

21 

25 

29 

23.5 

3 

4 

6 

8 

10 

11 

14 

17 

21 

25 

29 

24.0 

3 

4 

6 

8 

9 

11 

13 

17 

20 

24 

28 

24.5 

3 

4 

6 

8 

9 

10 

13 

16 

20 

24 

28 

25.0 

3 

4 

6 

8 

9 

10 

13 

16 

19 

23 

27 

25.5 

3 

4 

6 

8 

9 

10 

13 

16 

19 

23 

27 

26.0 

2 

4 

6 

8 

9 

10 

12 

15 

19 

22 

26 

26.5 

2 

4 

5 

7 

8 

10 

12 

15 

18 

22 

26 

27.0 

2 

4 

5 

7 

8 

9 

12 

15 

18 

21 

25 

27.5 

2 

4 

5 

7 

8 

9 

12 

15 

18 

21 

25 

28.0 

2 

4 

5 

7 

8 

9 

12 

14 

17 

21 

24 

28.5 

2 

4 

5 

7 

8 

9 

11 

14 

17 

20 

24 

29.0 

2 

3 

5 

7 

8 

9 

11 

14 

17 

20 

23 

29.5 

2 

3 

5 

7 

8 

9 

11 

14 

16 

20 

23 

30.0 

2 

3 

5 

7 

8 

9 

11 

13 

16 

19 

23 

30.5 

2 

3 

5 

6 

7 

8 

11 

13 

16 

19 

22 

310 

2 

3 

5 

6 

7 

8 

10 

13 

16 

19 

22 

31.5 

2 

3 

5 

6 

7 

8 

10 

13 

15 

18 

21 

32.0 

2 

3 

5 

6 

7 

8 

10 

13 

15 

18 

21 

32.5 

2 

3 

4 

6 

7 

8 

10 

12 

15 

18 

21 

33.0 

2 

3 

4 

6 

7 

8 

10 

12 

15 

17 

20 

33.5 

2 

3 

4 

6 

7 

8 

10 

12 

14 

17 

20 

34.0 

2 

3 

4 

6 

7 

8 

10 

12 

14 

17 

20 

34.5 

2 

3 

4 

6 

7 

7 

9 

12 

14 

17 

20 

35.0 

2 

3 

4 

6 

6 

7 

9 

11 

14 

16 

19 

35.5 

2 

3 

4 

6 

6 

7 

9 

11 

14 

16 

19 

36.0 

2 

3 

4 

5 

6 

7 

9 

11 

13 

16 

19 

36.5 

2 

3 

4 

5 

6 

7 

9 

11 

13 

16 

19 

37.0 

2 

3 

4 

5 

6 

7 

9 

11 

13 

16 

18 

37.5 

2 

3 

4 

5 

6 

7 

9 

11 

13 

15 

18 

38.0 

2 

3 

4 

5 

6 

7 

9 

11 

13 

15 

18 

38.5 

2 

3 

4 

5 

6 

7 

8 

10 

13 

15 

18 

39.0 

2 

3 

4 

5 

6 

7 

8 

10 

12 

15 

17 

39.5 

2 

3 

4 

5 

6 

6 

8 

10 

12 

15 

17 

40.0 

2 

3 

4 

5 

6 

6 

8 

10 

12 

14 

17 

40.5 

2 

2 

4 

5 

6 

6 

8 

10 

12 

14 

17 

41.0 

2 

2 

4 

5 

5 

6 

8 

10 

12 

14 

16 

41.5 

2 

2 

3 

5 

5 

6 

8 

10 

12 

14 

16 

VALUES  OF  L-  L=L«»"hi'»:"'- 

r2  r=  Radius  of  Gyration  in  Inches. 

LENGTH  IN  FEET 

r2 

in 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

Inches 

40 

46 

53 

59 

66 

74 

82 

90 

99 

109 

118 

128 

19.5 

39 

45 

51 

58 

65 

72 

80 

88 

97 

106 

115 

125 

20.0 

38 

44 

50 

56 

63 

70 

78 

86 

94 

103 

112 

122 

20.5 

37 

43 

49 

55 

62 

69 

76 

84 

92 

101 

110 

119 

21.0 

36 

42 

48 

54 

60 

67 

74 

82 

90 

98 

107 

116 

21.5 

36 

41 

47 

53 

59 

66 

73 

80 

88 

96 

105 

114 

22.0 

35 

40 

46 

51 

58 

64 

71 

78 

86 

94 

102 

111 

22.5 

34 

39 

45 

50 

56 

63 

70 

77 

84 

92 

100 

109 

23.0 

33 

38 

44 

49 

55 

61 

68 

75 

82 

90 

98 

106 

23.5 

33 

38 

43 

48 

54 

60 

67 

74 

81 

88 

96 

104 

24.0 

32 

37 

42 

47 

53 

59 

65 

72 

79 

86 

94 

102 

24.5 

31 

36 

41 

46 

52 

58 

64 

71 

77 

85 

92 

100 

25.0 

31 

35 

40 

45 

51 

57 

63 

69 

76 

83 

90 

98 

25.5 

30 

35 

39 

44 

50 

56 

62 

68 

74 

81 

89 

96 

26.0 

30 

34 

39 

44 

49 

54 

60 

67 

73 

80 

87 

94 

26.5 

29 

33 

38 

43 

48 

53 

59 

65 

72 

78 

85 

93 

27.0 

29 

33 

37 

42 

47 

53 

58 

64 

70 

77 

84 

91 

27.5 

28 

32 

37 

41 

46 

52 

57 

63 

69 

76 

82 

89 

28.0 

28 

32 

36 

41 

45 

51 

56 

62 

68 

74 

81 

88 

28.5 

27 

31 

35 

40 

45 

50 

55 

61 

67 

73 

79 

86 

29.0 

27 

31 

35 

39 

44 

49 

54 

60 

66 

72 

78 

85 

29.5 

26 

30 

34 

39 

43 

48 

53 

59 

65 

71 

77 

83 

30.0 

26 

30 

34 

38 

42 

47 

52 

58 

63 

69 

76 

82 

30.5 

25 

29 

33 

37 

42 

47 

52 

57 

62 

68 

74 

81 

31.0 

25 

29 

33 

37 

41 

46 

51 

56 

61 

67 

73 

79 

31,5 

25 

28 

32 

36 

41 

45 

50 

55 

61 

66 

72 

78 

32.0 

24 

28 

32 

36 

40 

44 

49 

54 

60 

65 

71 

77 

32.5 

24 

27 

31 

35 

39 

44 

48 

53 

59 

64 

70 

76 

33.0 

23 

27 

31 

35 

39 

43 

48 

53 

58 

63 

69 

75 

33.5 

23 

26 

30 

34 

38 

42 

47 

52 

57 

62 

68 

74 

34.0 

23 

26 

30 

34 

38 

42 

46 

51 

56 

61 

67 

72 

34.5 

22 

26 

29 

33 

37 

41 

46 

50 

55 

60 

66 

71 

350 

22 

25 

29 

33 

37 

41 

45 

50 

55 

60 

65 

70 

35.5 

22 

25 

28 

32 

36 

40 

44 

49 

54 

59 

64 

69 

36.0 

21 

25 

28 

32 

36 

40 

44 

48 

53 

58 

63 

69 

36.5 

21 

24 

28 

31 

35 

39 

43 

48 

52 

57 

62 

68 

37.0 

21 

24 

27 

31 

35 

39 

43 

47 

52 

56 

61 

67 

375 

21 

24 

27 

30 

34 

38 

42 

46 

51 

56 

61 

66 

38.0 

20 

23 

27 

30 

34 

38 

42 

46 

50 

55 

60 

65 

38.5 

20 

23 

26 

30 

33 

37 

41 

45 

50 

54 

59 

64 

39.0 

20 

23 

26 

29 

33 

37 

41 

45 

49 

54 

58 

63 

39.5 

20 

23 

26 

29 

32 

36 

40 

44 

48 

53 

58 

63 

40.0 

19 

22 

25 

29 

32 

36 

40 

44 

48 

52 

57 

62 

40.5 

19 

22 

25 

28 

32 

35 

39 

43 

47 

52 

56 

61 

41.0 

19 

22 

25 

28 

31 

35 

39 

43 

47 

51 

56 

60 

41.5 

93 


VALUES  OF^     L=Un9lh  inF'et 

r2     r  -  Radius  of  Gyration  in  Inches. 

r2 

LENGTH  IN  FEET. 

in 

Inches 

8 

10 

12 

14 

15 

16 

18 

20 

22 

24 

26 

42.0 

2 

2 

3 

5 

5 

6 

8 

10 

12 

14 

16 

42.5 

2 

2 

3 

5 

5 

6 

8 

9 

11 

14 

16 

43.0 

1 

2 

3 

5 

5 

6 

8 

9 

11 

13 

16 

43.5 

1 

2 

3 

5 

5 

6 

7 

9 

11 

13 

16 

44.0 

1 

2 

3 

4 

5 

6 

7 

9 

11 

13 

15 

44.5 

1 

2 

3 

5 

6 

7 

9 

11 

'  13 

15 

45.0 

1 

2 

3 

5 

6 

7 

9 

11 

13 

15 

45.5 

1 

2 

3 

5 

6 

7 

9 

11 

13 

15 

46.0 

1 

2 

3 

5 

5 

7 

9 

11 

13 

15 

46.5 

1 

2 

3 

5 

5 

7 

9 

10 

12 

15 

47.0 

1 

2 

3 

5 

5 

7 

9 

10 

12 

14 

47.5 

1 

2 

3 

5 

5 

7 

8 

10 

12 

14 

48.0 

1 

2 

3 

5 

5 

7 

8 

10 

12 

14 

485 

1 

2 

3 

5 

5 

7 

8 

10 

12 

14 

49.0 

1 

2 

3 

5 

5 

7 

8 

10 

12 

14 

49.5 

1 

2 

3 

4 

5 

5 

7 

8 

9 

12 

14 

50.0 

1 

2 

3 

4 

5 

5 

6 

8 

9 

12 

14 

50.5 

1 

2 

3 

4 

5 

5 

6 

8 

9 

11 

13 

51.0 

1 

2 

3 

4 

4 

5 

6 

8 

9 

11 

13 

51.5. 

1 

2 

3 

4 

4 

5 

6 

8 

9 

11 

13 

52.0 

1 

2 

3 

4 

4 

5 

6 

8 

9 

11 

13 

52.5 

1 

2 

3 

4 

4 

5 

6 

8 

9 

11 

13 

53.0 

1 

2 

3 

4 

4 

5 

6 

8 

9 

11 

13 

53.5 

1 

2 

3 

4 

4 

5 

6 

7 

9 

11 

13 

54.0 

1 

2 

3 

4 

4 

5 

6 

7 

9 

11 

13 

54.b 

1 

2 

3 

4 

4 

5 

6 

7 

9 

11 

12 

55.0 

1 

2 

3 

4 

5 

6 

7 

9 

10 

12 

55.5 

1 

2 

3 

4 

5 

6 

7 

9 

10 

12 

56.0 

1 

2 

3 

3 

5 

6 

7 

9 

10 

12 

56.5 

1 

2 

3 

3 

5 

6 

7 

9 

10 

12 

57.0 

1 

2 

3 

3 

6 

7 

8 

10 

12 

57.5 

1 

2 

3 

3 

6 

7 

8 

10 

12 

53.0 

1 

2 

2 

3 

6 

7 

8 

10 

12 

58.5 

1 

2 

2 

3 

6 

7 

8 

10 

12 

59.0 

1 

2 

2 

3 

5 

7 

8 

10 

11 

59.5 

1 

2 

2 

3 

5 

7 

8 

10 

11 

60,0 

1 

2 

2 

3 

5 

7 

8 

10 

11 

60.5 

1 

2 

2 

3 

5 

7 

8 

10 

11 

61.0 

1 

2 

2 

3 

5 

7 

8 

9 

11 

61.5 

1 

2 

2 

3 

5 

7 

8 

9 

11 

62.0 

1 

2 

2 

3 

5 

6 

8 

9 

11 

62.5 

1 

2 

2 

3 

5 

6 

8 

9 

11 

63.0 

1 

2 

2 

3 

5 

6 

8 

9 

11 

63.5 

1 

2 

2 

3 

5 

6 

8 

9 

11 

64.0 

1 

2 

2 

3 

4 

5 

6 

8 

9 

11 

1 

L-  L  -Length  in  Feet. 
VALUES  OF  — 
r-  r  Radius  of  Gyration  in  Inches. 

LENGTH  IN  FEET 

r2 

in 

28 

30 

32 

34 

36 

33 

40 

42 

44 

46 

48 

50 

Inches 

19 

21 

24 

28 

31 

34 

38 

42 

46 

50 

55 

60 

42.0 

18 

21 

24 

27 

30 

34 

38 

42 

46 

50 

54 

59 

42.5 

18 

21 

24 

27 

30 

34 

37 

41 

45 

49 

54 

58 

430 

18 

'  21 

24 

27 

30 

33 

37 

41 

45 

49 

53 

57 

43.5 

18 

20 

23 

26 

29 

33 

36 

40 

44 

48 

52 

57 

44.0 

13 

20 

23 

26 

29 

32 

36 

40 

44 

48 

52 

56 

44.5 

17 

20 

23 

26 

29 

32 

36 

39 

43 

47 

51 

56 

45.0 

17 

20 

23 

25 

28 

32 

35 

39 

43 

47 

51 

55 

45.5 

17 

20 

22 

25 

28 

31 

35 

38 

42 

46  ' 

50 

54 

46.0 

17 

19 

22 

25 

28 

31 

34  • 

38 

42 

45 

50 

54 

46.5 

17 

19 

22 

25 

28 

31 

34 

38 

41 

45 

49 

53 

47.0 

17 

19 

22 

24 

27 

30 

34 

37 

41 

45 

49 

53 

47.5 

16 

19 

21 

24 

27 

30 

33 

37 

40 

44 

48 

52 

48.0 

16 

19 

21 

24 

27 

30 

33 

36 

40 

44 

48 

52 

48.5 

16 

18 

21 

24 

26 

29 

33 

36 

40 

43 

47 

51 

49.0 

16 

18 

21 

23 

26 

29 

32 

36 

39 

43 

47 

51 

49.5 

16 

18 

20 

23 

26 

29 

32 

35 

39 

42 

46 

50 

50.0 

16 

18 

20 

23 

26 

29 

32 

35 

38 

42 

46 

50 

50.5 

15 

18 

20 

23 

25 

28 

31 

35 

38 

41 

45 

49 

51.0 

15 

17 

20 

22 

25 

28 

31 

34 

38 

41 

45 

49 

51.5 

15 

17 

20 

22 

25 

28 

31 

34 

37 

41 

44 

48 

52.0 

15 

17 

20 

22 

25 

28 

30 

34 

37 

40 

44 

48 

52.5 

15 

17 

19 

22 

24 

27 

30 

33 

37 

40 

43 

47 

53.0 

15 

17 

19 

22 

24 

27 

30 

33 

36 

40 

43 

47 

53.5 

15 

17 

19 

21 

24 

27 

30 

33 

36 

39 

43 

46 

54.0 

14 

17 

19 

21 

24 

26 

29 

32 

36 

39 

42 

46 

54.5 

14 

16 

19 

21 

24 

26 

29 

32 

35 

38 

42 

45 

55.0 

14 

16 

18 

21 

23 

26 

29 

32 

35 

38 

42 

45 

55.5 

14 

16 

18 

21 

23 

26 

29 

31 

35 

38 

41 

45 

56.0 

14 

16 

18 

20 

23 

26 

28 

31 

34 

37 

41 

44 

56.5 

14 

16 

18 

20 

23 

25 

28 

31 

34 

37 

40 

44 

570 

14 

16 

18 

20 

23 

25 

28 

31 

34 

37 

40 

43 

57.5 

14 

16 

18 

20 

22 

25 

28 

30 

33 

36 

40 

43 

58.0 

13 

15 

18 

20 

22 

25 

27 

30 

33 

36 

39 

43 

585 

13 

15 

17 

20 

22 

24 

27 

30 

33 

36 

39 

42 

59.0 

13 

15 

17 

19 

22 

24 

27 

30 

33 

36 

39 

42 

59.5 

13 

15 

17 

19 

22 

24 

27 

29 

32 

35 

38 

42 

600 

13 

15 

17 

19 

21 

24 

26 

29 

32 

35 

38 

41 

60.5 

13 

15 

17 

19 

21 

24 

26 

29 

32 

35 

38 

41 

61.0 

13 

15 

17 

19 

21 

23 

26 

29 

31 

34 

37 

41 

61.5 

13 

15 

17 

19 

21 

23 

26 

28 

31 

34 

37 

40 

62.0 

13 

14 

16 

18 

21 

23 

26 

28 

31 

34 

37 

40 

62.5 

12 

14 

16 

18 

21 

23 

25 

28 

31 

34 

37 

40 

63.0 

12 

14 

16 

18 

20 

23 

25 

28 

30 

33 

36 

39 

63.5 

12 

14 

16 

18 

20 

23 

25 

28 

30 

33 

36 

39 

64.0 

95 


VALUES  Opt!  «-=L.n,thinFee«. 

r-  r=Radius  of  Gyration  in  Inches. 

r2 

LENGTH  IN  FEET. 

in 

Inches 

14 

15 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

64.5 

3 

3 

4 

5 

6 

8 

9 

10 

12 

14 

16 

18 

20 

22 

25 

27 

30 

33 

36 

39 

65.0 

3 

3 

4 

5 

6 

7 

9 

10 

12 

14 

16 

18 

20 

22 

25 

27 

30 

33 

35 

38 

65.5 

3 

3 

4 

5 

6 

7 

9 

10 

12 

14 

16 

18 

20 

22 

24 

27 

30 

32 

35 

38 

66.0 

3 

3 

4 

5 

6 

7 

9 

10 

12 

14 

16 

18 

20 

22 

24 

27 

29 

32 

35 

38 

66.5 

3 

3 

4 

5 

6 

7 

9 

10 

12 

14 

15 

17 

19 

22 

24 

27 

29 

32 

35 

38 

670 

3 

3 

4 

5 

6 

7 

9 

10 

12 

13 

15 

17 

19 

22 

24 

26 

29 

32 

34 

37 

67.5 

3 

3 

4 

5 

6 

7 

9 

10 

12 

13 

15 

17 

19 

21 

24 

26 

29 

31 

34 

37 

68.0 

3 

3 

5 

6 

7 

8 

10 

12 

13 

15 

17 

19 

21 

24 

26 

28 

31 

34 

37 

68.5 

3 

3 

5 

6 

7 

8 

10 

11 

13 

15 

17 

19 

21 

23 

26 

28 

31 

34 

36 

69.0 

3 

3 

5 

6 

7 

8 

10 

11 

13 

15 

17 

19 

21 

23 

26 

28 

31 

33 

36 

69.5 

3 

3 

5 

6 

7 

8 

10 

11 

13 

15 

17 

19 

21 

23 

25 

28 

30 

33 

36 

70.0 

3 

3 

5 

6 

7 

8 

10 

11 

13 

15 

17 

19 

21 

23 

25 

28 

30 

33 

36 

70.5 

3 

3 

5 

6 

7 

8 

10 

11 

13 

15 

16 

18 

20 

23 

25 

27 

30 

33 

35 

71.0 

3 

3 

5 

6 

7 

8 

10 

11 

13 

14 

16 

18 

20 

23 

25 

27 

30 

32 

35 

71.5 

3 

3 

5 

6 

7 

8 

9 

11 

13 

14 

16 

18 

20 

22 

25 

27 

30 

32 

35 

72.0 

3 

3 

4 

5 

6 

7 

8 

9 

11 

13 

14 

16 

18 

20 

22 

25 

27 

29 

32 

35 

73.0 

3 

3 

4 

4 

5 

7 

8 

9 

11 

12 

14 

16 

18 

20 

22 

24 

27 

29 

32 

34 

74.0 

3 

3 

3 

4 

5 

7 

8 

9 

11 

12 

14 

16 

18 

20 

22 

24 

26 

29 

31 

34 

75.0 

3 

3 

3 

4 

5 

6 

8 

9 

10 

12 

14 

15 

17 

19 

21 

24 

26 

28 

31 

33 

76.0 

3 

3 

3 

4 

5 

6 

8 

9 

10 

12 

13 

15 

17 

19 

21 

23 

25 

28 

30 

33 

77.0 

3 

3 

3 

4 

5 

6 

7 

9 

10 

12 

13 

15 

17 

19 

21 

23 

25 

27 

30 

32 

78.0 

2 

3 

3 

4 

5 

6 

7 

9 

10 

12 

13 

15 

17 

19 

21 

23 

25 

27 

30 

32 

79.0 

3 

3 

4 

5 

6 

7 

9 

10 

11 

13 

15 

16 

18 

20 

22 

25 

27 

29 

32 

80.0 

3 

3 

4 

5 

6 

7 

8 

10 

11 

13 

14 

16 

18 

20 

22 

24 

26 

29 

31 

81.0 

3 

3 

4 

5 

6 

7 

8 

10 

11 

13 

14 

16 

18 

20 

22 

24 

26 

28 

31 

82.0 

3 

3 

4 

5 

6 

7 

8 

10 

11 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

84.0 

3 

3 

4 

5 

6 

7 

8 

9 

11 

12 

14 

15 

17 

19 

21 

23 

25 

27 

30 

86.0 

3 

3 

4 

5 

6 

7 

8 

9 

10 

12 

13 

15 

17 

19 

21 

23 

25 

27 

29 

88.0 

3 

3 

4 

5 

6 

7 

8 

9 

10 

12 

13 

15 

16 

18 

20 

22 

24 

26 

28 

90.0 

3 

3 

4 

4 

5 

6 

8 

9 

10 

11 

13 

14 

16 

18 

20 

22 

24 

26 

28 

92.0 

2 

3 

4 

4 

5 

6 

7 

9 

10 

11 

13 

14 

16 

17 

19 

21 

23 

25 

27 

94.0 

3 

3 

4 

5 

6 

7 

8 

10 

11 

12 

14 

15 

17 

19 

21 

23 

25 

27 

96.0 

3  3 

4 

5 

6 

7 

8 

9 

11 

12 

14 

15 

17 

18 

20 

22 

24 

26 

98.0 

3 

3 

4 

5 

6 

7 

8 

9 

10 

12 

13 

15 

16 

18 

20 

22 

24 

26 

100.0 

3 

3 

4 

5 

6 

7 

8 

9 

10 

12 

13 

14 

16 

18 

19 

21 

23 

26 

102.0 

3 

3 

4 

5 

6 

7 

8 

9 

10 

11 

13 

14 

16 

17 

19 

21 

23 

25 

104.0 

2 

3 

4 

5 

6 

7 

7 

9 

10 

11 

12 

14 

15 

17 

19 

20 

22 

24 

106.0 

3 

4 

5 

5 

6 

7 

8 

10 

11 

12 

14 

15 

17 

18 

20 

22 

24 

103.0 

3 

4 

4 

5 

6 

7 

8 

9 

11 

12 

13 

15 

16 

18 

20 

21 

23 

110.0 

3 

4 

4 

5 

6 

7 

8 

9 

11 

12 

13 

15 

16 

18 

19 

21 

23 

112.0 

3 

4 

4 

5 

6 

7 

8 

9 

10 

12 

13 

14 

16 

17 

19 

21 

22 

114.0 

3 

4 

4 

5 

6 

7 

8 

9 

10 

11 

13 

14 

15 

17 

19 

20 

22 

116.0 

3 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

14 

15 

17 

18 

20 

22 

118.0 

3 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

14 

15 

16 

18 

20 

21 

120.0 

3 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

15 

16 

18 

19 

21 

WORKING  STRENGTHS  OF  SOFT  STEEL  COLUMNS. 

Square  Bearing    Pin  and  Square  Bearing     Pin  Bearing 

12500      o     12500           12500 

5   i+    /2     "    i+    /2         i+    /2 

36000  r2         24000  r2          iSooor2 

Where  :  — 

S  =  Working  strengths  in  Ibs.  per  square  inch. 

L  =  Length  in  feet. 
/  =  Length  in  inches. 

r  =  Least  radius  of  gyration  in  inches. 

WORKING  STRENGTHS 

WORKING  STRENGTHS 

L2 

Us.  per  Sq.  In. 

L2 

Lbs.  per  Sq.  In. 

r2 

Square 

Pin  and 
Square 

Pin 

r2 

Square 

Pin  and 
Square 

Pin 

l 

12495 

12426 

12402 

26 

11323 

10813 

10348 

2 

12402 

12352 

12304 

27 

11282 

10757 

10280 

3 

12352 

12280 

12208 

28 

11241 

10702 

10213 

4 

12304 

12208 

12113 

29 

11201 

10647 

10146 

5 

12255 

12137 

12020 

30 

11161 

10593 

10081 

6 

12208 

12067 

11929 

31 

11121 

10540 

10016 

7 

12160 

11997 

11838 

32 

11082 

10487 

9952 

8 

12112 

11928 

11748 

33 

11043 

10434 

9889 

9 

12065 

11860 

11660 

34 

11004 

10382 

9827 

10 

12019 

11793 

11575 

35 

10965 

10331 

9766 

11 

11973 

11726 

11490 

36 

10927 

10280 

9705 

12 

11927 

11660 

11406 

37 

10888 

10229 

9645 

13 

11882 

11596 

11323 

38 

10851 

10179 

9586 

14 

11837 

11532 

11241 

39 

10813 

10130 

9527 

15 

11792 

11468 

11161 

40 

10776 

10081 

9469 

15 

11748 

11405 

11082 

41 

10739 

10032 

9412 

17 

11704 

11343 

11003 

42 

10702 

9984 

9355 

18 

11660 

11282 

10927 

43 

10666 

9936 

9301 

19 

11617 

11221 

10852 

44 

10629 

9889 

9246 

20 

11574 

11161 

10776 

45 

10592 

9842 

9191 

21 

11531 

11102 

10702 

46 

10557 

9796 

9137 

22 

11489 

11043 

10629 

47 

10522 

9750 

9084 

23 

11447 

10984 

10557 

48 

10486 

9705 

9032 

24 

11405 

10927 

10487 

49 

10451 

9660 

8980 

25 

11364 

10870 

10417 

50 

10416 

9615 

8928 

97 


WORKING  STRENGTHS  OF  SOFT  STEEL  COLUMNS. 

(CONTINUED.) 


WORKING  STRENGTHS 

WORKING  STRENGTHS 

L2 

Lbs.  per  Sq.  Inch. 

L2 

Lbs.  per  Sq.  Inch. 

r* 

Square 

Pin  and 
Square 

Pin 

r2 

Square 

Pin  and 
Square 

Pin 

51 

10382 

9571 

8878 

86 

9300 

8245 

7405 

52 

10348 

9528 

8828 

87 

9273 

8213 

7370 

53 

10314 

9484 

8778 

88 

9246 

8181 

7335 

54 

10280 

9441 

8728 

89 

9219 

8149 

7301 

55 

10246 

.  9398 

8680 

90 

9192 

8117 

7267 

56 

10212 

9355 

8633 

91 

9165 

8085 

7233 

57 

10179 

9314 

8585 

92 

9138 

8054 

7200 

58 

10146 

9273 

8538 

93 

9111 

8023 

7168 

59 

10113 

9232 

8492 

94 

9084 

7992 

7135 

60 

10081 

9191 

8446 

95 

9058 

7962 

7102 

61 

10048 

9151 

8401 

96 

9032 

7931 

7070 

62 

10016 

9111 

8356 

97 

9006 

7901 

7038 

63 

9984 

9071 

8311 

98 

8980 

7871 

7007 

64 

9953 

9032 

8267 

99 

8954 

7842 

6975 

65 

9921 

8993 

8224 

100 

8928 

7813 

6944 

66 

9889 

8954 

8181 

101 

8903 

7783 

6914 

67 

9858 

8916 

8138 

102 

8878 

7754 

6883 

68 

9827 

8878 

8096 

103 

8853 

7726 

6853 

69 

9796 

8840 

8054 

104 

8828 

7697 

6823 

70 

9766 

8803 

8013 

105 

8803 

7669 

6793 

71 

9735 

8766 

7972 

106 

8778 

7641 

6764 

72 

9705 

8729 

7932 

107 

8753 

7613 

6735 

73 

9675 

8693 

7892 

108 

8729 

7585 

6706 

74 

9645 

8657 

7852 

109 

8705 

7558 

6678 

75 

9615 

8621 

7813 

110 

8680 

7530 

6649 

76 

9586 

8585 

7774 

111 

8656 

7503 

6621 

77 

9557 

8550 

7735 

112 

8633  ' 

7476 

6593 

78 

9528 

8515 

7697 

113 

8609 

7449 

6565 

79 

9499 

8480 

7659 

114 

8585 

7423 

6533 

80 

9470 

8446 

7622 

115 

8562 

7397 

6510 

81 

9441 

8412 

7585 

116 

8538 

7370 

6483 

82 

9412 

8378 

7548 

117 

8515 

7344 

6457 

83 

9384 

8344 

7512 

118 

8492 

7318 

6430 

84 

9356 

8311 

7476 

119 

8469 

7293 

6404 

85 

9328 

8278 

7440 

120 

8446 

7268 

6378 

98 


WORKING  STRENGTHS  OF  SOFT  STEEL  COLUMNS. 

(CONTINUED.) 

WORKING  STRENGTHS 

WORKING  STRENGTHS 

L2 

Lbs.  per  Sq.  Inch. 

L2 

Lbs.  per  Sq.  Inch. 

r- 

Square 

Pin  and 
Square 

Pin 

r* 

Square 

Pin  and 

Square 

Pin 

121 

8423 

7242 

6352 

180 

7268 

6010 

5123 

122 

8401 

7217 

6326 

185 

7184 

5924 

5040 

123 

8378 

7192 

6300 

190 

7102 

5842 

4960 

124 

8356 

7168 

6275 

195 

7023 

5760 

4883 

125 

8333 

7143 

6250 

200 

6944 

5682 

4808 

126 

8311 

7118 

6225 

205 

6868 

5605 

4735 

127 

8289 

7094 

6200 

210 

6793 

5531 

4664 

128 

8267 

7070 

6176 

215 

6720 

5458 

4596 

129 

8245 

7046 

6152 

220 

6649 

5388 

4529 

130 

8224 

7023 

6127 

225 

6579 

5319 

4464 

131 

8202 

6999 

6103 

230 

6510 

5252 

4401 

132 

8181 

6975 

6080 

235 

6443 

5187 

4340 

133 

8159 

6952 

6056 

240 

6378 

5123 

4281 

134 

8138 

6929 

6033 

245 

6313 

5061 

4223 

135 

8117 

6906 

6010 

250 

6250 

5000 

4167 

136 

8096 

6883 

5987 

255 

6188 

4941 

4112 

137 

8075 

6861 

5964 

260 

6128 

4883 

4058 

138 

8054 

6838 

5941 

265 

6068 

4826 

4007 

139 

8033 

6816 

5918 

270 

6010 

4771 

3956 

140 

8013 

6793 

5896 

275 

5952 

4717 

3906 

141 

7992 

6771 

5874 

280 

51896 

4664 

3858 

142 

7972 

6749 

5852 

285 

5841 

4612 

3811 

143 

7952 

6728 

5830 

290 

5787 

4562 

3?£5 

144 

7932 

6706 

5808 

295 

5734 

4513 

3720 

145 

7912 

6684 

5787 

300 

5682 

4464 

3677 

146 

7892 

6633 

5766 

310 

5580 

4371 

3592 

147 

7872 

6642 

5744 

320 

5483 

4281 

3511 

148 

7852 

6621 

5723 

330 

5388 

4195 

3434 

149 

7832 

6600 

5702 

340 

5297 

4112 

3360 

150 

7813 

6579 

5682 

350 

5209 

4032 

3288 

155 

7716 

6477 

5580 

360 

5123 

3956 

3222 

160 

7622 

6378 

5482 

370 

5040 

3882 

3157 

165 

7530 

6282 

5388 

380 

4960 

3811 

3094 

170 

7441 

6188 

5297 

390 

4883 

3742 

3034 

175 

7353 

6098 

5208 

400 

4808 

3676 

2976 

99 


WORKING  STRENGTHS  OF  MEDIUM  STEEL  COLUMNS. 

Square  Bearing    Pin  and  Square  Bearing     Pin  Bearing 

15000           15000      o     15000 

«              72       »              72       *->  —            72 

I  +                     1  +                     I  +      ' 

36ooor2         24000  r2          iSooor* 

Where  :  — 

S  =  Working  strengths  in  Ibs.  per  square  inch. 
L  =  Length  in  feet. 

/  =  Length  in  inches. 
r  —  Least  radius  of  gyration  in  inches. 

WORKING  STRENGTHS 

WORKING  STRENGTHS 

L2 

Lbs.  per  Sq.  In. 

L2 

Lbs.  per  Sq.  In. 

r2 

Square 

Pin  and 

Square 

Pin 

r2 

Square 

Pin  and 

Square 

Pin 

l 

14940 

14910 

14881 

26 

13587 

12976 

12417 

2 

14881 

14822 

14764 

27 

13538 

12909 

12336 

3 

14822 

14735 

14649 

28 

13489 

12843 

12255 

4 

14764 

14649 

14535 

29 

13441 

12777 

12175 

5 

14706 

14563 

14423 

30 

13393 

12712 

12097 

6 

14648 

14479 

14313 

31 

13345 

12648 

12019 

7 

14591 

14396 

14205 

32 

13298 

12584 

11943 

8 

14535 

14313 

14098 

33 

13251 

12521 

11867 

9 

14479 

14232 

13992 

34 

13204 

12459 

11793 

10 

14423 

14151 

13889 

35 

13157 

12397 

11719 

11 

14368 

14071 

13787 

36 

13112 

12336 

11646 

12 

14313 

13992 

13686 

37 

13066 

12275 

11574 

13f 

14259 

13915 

13587 

38 

13021 

12215 

11503 

14 

15205 

13838 

13489 

39 

12976 

12155 

11433 

15 

14151 

13761 

13393 

40 

12931 

12097 

11364 

16 

14098 

13686 

13298 

41 

12887 

12039 

11295 

17 

14045 

13612 

13204 

42 

12843 

11981 

11228 

18 

13992 

13538 

13112 

43 

12799 

11924 

11161 

19 

13940 

13465 

13021 

44 

12755 

11867 

11095 

20 

13889 

13393 

12931 

45 

12712 

11811 

11030 

21 

13838 

13322 

12843 

46 

12669 

11756 

10965 

22 

13787 

13251 

12755 

47 

12626 

11700 

10901 

23 

13736 

13181 

12669 

48 

12583 

11646 

10838 

24 

13686 

13112 

12584 

49 

12542 

11592 

10776 

25 

13637 

13044 

12500 

50 

12500 

11538 

10714 

WORKING  STRENGTHS  OF  MEDIUM  STEEL  COLUMNS. 

(CONTINUED.) 

L2 

WORKING  STRENGTHS 
Lbs.  per  Sq.  Inch. 

L2 

WORKING  STRENGTHS 
Lbs.  per  Sq.  Inch. 

r2 

Square 

Pin  and 
Square 

Pin 

r2 

Square 

Pin  and 

Square 

Pin 

51 

1245.9 

11486 

10653 

86 

11161 

9894 

8886 

52 

12417 

11433 

10593 

87 

11128 

9855 

8844 

53 

12376 

11381 

10534 

88 

11095 

9817 

8803 

54 

12336 

11329 

10475 

89 

11062 

9779 

8762 

55 

12295 

11278 

10417 

90 

11030 

9740 

8721 

56 

12255 

11227 

10359 

91 

10997 

9702 

8680 

57 

12215 

11177 

10302 

92 

10965 

9665 

8640 

58 

12176 

11128 

10246 

93 

10933 

9628 

8601 

59 

12136 

11078 

10190 

94 

10901 

9591 

8562 

60 

12097 

11030 

10135 

95 

10870 

9554 

8523 

61 

12058 

10981 

10081 

96 

10838 

9518 

8484 

62 

12019 

10933 

10027 

97 

10807 

9482 

8446 

63 

11981 

10886 

9974 

98 

10776 

9446 

8408 

64 

11943 

10838 

9921 

99 

10745 

9410 

8370 

65 

11905 

10791 

9869 

100 

10714 

9375 

8333 

66 

11867 

10745 

9817 

101 

10684 

9340 

8297 

67 

11830 

10699 

9766 

102 

10653 

9305 

8260 

68 

11793 

10653 

9715 

103 

10623 

9271 

8224 

69 

11756 

10608 

9665 

104 

10593 

9237 

8188 

70 

11719 

10563 

9615 

105 

10563 

9202 

8152 

71 

11682 

10519 

9566 

106 

10534 

9169 

8117 

72 

11646 

10475 

9518 

107 

10504 

9135 

8082 

73 

11610 

10431 

9470 

108 

10475 

9102 

8047 

74 

11574 

10388 

9422 

109 

10446 

9069 

8013 

75 

11538 

10345 

9375 

110 

10417 

9036 

7979 

76 

11503 

10302 

9329 

111 

10388 

9003 

7945 

77 

11468 

10260 

9282 

112 

10359 

8971 

7911 

78 

11433 

10218 

9236 

113 

10330 

8930 

7878 

79 

11398 

10176 

9191 

114 

10302 

8907 

7845 

80 

11364 

10135 

9146 

115 

10274 

8876 

7812 

81 

11329 

10094 

9102 

116 

10246 

8844 

7780 

82 

11295 

10053 

9058 

117 

10218 

8813 

7748 

83 

11261 

10013 

9014 

118 

10190 

8782 

7716 

84 

11227 

9973 

8971 

119 

10163 

8751 

7685 

85 

11194 

9934 

8928 

120 

10135 

8721 

7653 

WORKING  STRENGTHS  OF  MEDIUM  STEEL  COLUMNS. 

(CONTINUED.) 

WORKING  STRENGTHS 

WORKING  STRENGTHS 

L2 

Lbs.  per  Sq.  Inch. 

L2 

Lbs.  per  Sq.  Inch. 

r* 

Square 

Pin  and 

Square 

Pin 

r2 

Square 

Pin  and 

Square 

Pin 

121 

10108 

8691 

7622 

180 

8721 

7212 

6143 

122 

10081 

8661 

7591 

185 

8621 

7109 

6048 

123 

10054 

8631 

7560 

190 

8523 

7010 

5952 

124 

10027 

8601 

7530 

195 

8427 

6912 

5859 

125 

10000 

8571 

7500 

200 

8333 

6818 

5769 

126 

9974 

8542 

7470 

205 

8242 

6726 

5682 

127 

9947 

8513 

7440 

210 

8152 

6637 

5597 

128 

9921 

8484 

7411 

215 

8064 

6550 

5515 

129 

9894 

8456 

7382 

220 

7979 

6465 

5435 

130 

9868 

8427 

7353 

?25 

7895 

6383 

5357 

131 

9843 

8399 

7324 

230 

7812 

6303 

5282 

132 

9817 

8370 

7296 

235 

7732 

6224 

5208 

133 

9791 

8343 

7268 

240 

7653 

6148 

5137 

134 

9766 

8315 

7239 

245 

7575 

6073 

5067 

135 

9740 

8287 

7212 

250 

7500 

6000 

5000 

136 

9715 

8260 

7184 

255 

7426 

5929 

4934 

137 

9690 

8233 

7157 

260 

7353 

5859 

4870 

138 

9665 

8206 

7129 

265 

7281 

5791 

4808 

139 

9640 

8179 

7102 

270 

7212 

5725 

4747 

140 

9615 

8152 

7076 

275 

7143 

5660 

4668 

141 

9591 

8126 

7049 

280 

7076 

5597 

4630 

142 

9566 

8099 

7023 

285* 

7010 

5535 

4573 

143 

9542 

8073 

6996 

290 

6945 

5475 

4518 

144 

9518 

8047 

6970 

295 

6881 

5415 

4464 

145 

9494 

8021 

6945 

300 

6818 

5357 

4412 

146 

9470 

7996 

6919 

310 

6696 

5245 

4311 

147 

9446 

7970 

6893 

320 

6579 

5137 

4214 

148 

9422 

7945 

6868 

330 

6465 

5034 

4121 

149 

9399 

7919 

6843 

340 

6356 

4934 

4032 

150 

9375 

7895 

6818 

350 

6250 

4839 

3947 

155 

9259 

7772 

6696 

360 

6147 

4747 

3866 

160 

9146 

7653 

6579 

370 

6048 

4658 

3788 

165 

9036 

7538 

6465 

380 

5952 

4573 

3713 

170 

8929 

7426 

6356 

390 

5859 

4491 

3641 

175 

8823 

7317 

6250 

400 

5769 

4412 

3572 

TABLE  OF  SQUARE   ROOTS. 

IN. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

i 

1.00 

51 

7.14 

101 

10.05 

151 

12.29 

201 

14.18 

2 

1.41 

52 

7.21 

102 

10.10 

152 

12.33 

202 

14  21 

3 

1.73 

53 

7.28 

103 

10.15 

153 

12.37 

203 

14.25 

4 

2.00 

54 

7.35 

104 

10  20 

154 

12.41 

204 

14.28 

5 

2.24 

55 

7.42 

105 

10.25 

155 

12.45 

205 

14.32 

6 

2.45 

56 

7.48 

106 

10.30 

156 

12.49 

206 

14.35   . 

7 

2.65 

57 

7.55 

107 

10.34 

157 

12.53 

207 

14.39 

8 

2.83 

58 

762 

108 

10.39 

158 

12.57 

208 

14.42 

9 

3.00 

59 

7.68 

109 

10.44 

159 

12.61 

209 

14.46 

10 

3.16 

60 

7.75 

110 

10.49 

160 

12.65 

210 

14.49 

11 

3.32 

61 

7.81 

111 

10.54 

161 

12.69 

211 

14.53 

12 

3.46 

62 

7.87 

112 

10.58 

162 

12.73 

212 

14.56 

13 

3.61 

63 

7.94 

113 

10.63 

163 

12.77 

213 

14.59 

14 

3.74 

64 

8.00 

114 

10.68 

164 

12  81 

214 

14.63 

15 

3.87 

65 

8.06 

115 

10.72 

165 

12.85 

215 

14.66 

16 

4.00 

66 

8.12 

116 

10.77 

166 

12.88 

216 

14.70 

17 

4  12 

67 

8.19 

117 

10.82 

167 

12.92 

217 

1473 

18 

4.24 

68 

825 

118 

10.86 

168 

12.96 

218 

14.76 

19 

4.36 

69 

831 

119 

10.91 

169 

13.00 

219 

14.80 

20 

4.47 

70 

8.37 

120 

10.95 

170 

13.04 

220 

14.83 

21 

4.58 

71 

843 

121 

11.00 

171 

13.08 

221 

14.87 

22 

4.69 

72 

8.49 

122 

11.05 

172 

13.11 

222 

14.90 

23 

4.80 

73 

8.54 

123 

11.09 

173 

13.15 

223 

14.93 

24 

4.90 

74 

8.60 

124 

11.14 

174 

13.19 

224 

14.97 

25 

5.00 

75 

8.66 

125 

11.18 

175 

13.23 

225 

1500 

26 

5.10 

76 

8.72 

126 

11.22 

176 

13.27 

226 

15.03 

27 

5.20 

77 

8.77 

127 

11.27 

177 

13.30 

227 

15.07 

28 

5.29 

78 

8.83 

128 

11.31 

178 

13.34 

228 

15.10 

29 

5.39 

79 

8.89 

129 

11.36 

179 

13.38 

229 

15.13 

30 

5.48 

80 

8.94 

130 

11.40 

180 

13.42 

230 

15.17 

31 

5.57 

81 

9.00 

131 

11.45 

181 

13.45 

231 

15.20 

32 

5.66 

82 

9.06 

132 

11.49 

182 

13-49 

232 

15.23 

33 

574 

83 

9.11 

133 

11.53 

183 

1353 

233 

1526 

34 

5.83 

84 

9.17 

134 

11.58 

184 

13  56 

234 

1530 

35 

5.92 

85 

9.22 

135 

11.62 

185 

13.60 

235 

15.33 

36 

600 

•86 

9.27 

136 

11.66 

186 

13.64 

236 

15.36 

37 

608 

87 

9.33 

137 

11.70 

187 

1367 

237 

1539 

38 

6  16 

88 

9.38 

138 

11.75 

188 

13.71 

238 

1543 

39 

624 

89 

943 

139 

11.79 

189 

1375 

239 

15.46 

40 

632 

90 

9.49 

140 

11.83 

190 

13  78 

240 

1549 

41 

640 

91 

954 

141 

11.87 

191 

1382 

241 

15.52 

42 

6.48 

92 

9.59 

142 

1192 

192 

13.86 

242 

15.56 

43 

656 

93 

964 

143 

11.96 

193 

13.89 

243 

15.59 

44 

663 

94 

9.70 

144 

1200 

194 

1393 

244 

15.62 

45 

6.71 

95 

9.75 

145 

12.04 

195 

13.96 

245 

15.65 

46 

678 

96 

980 

146 

12.08 

196 

14.00 

246 

1568 

47 

686 

97 

9.85 

147 

12.12 

197 

14.04 

247 

15.72 

48 

6.93 

98 

9.90 

148 

12.17 

198 

14.07 

248 

15.75 

49 

700 

99 

9  95 

149 

12  21 

199 

14.11 

249 

15.78 

50 

7.C7 

100 

10.00 

150 

12.25 

200 

14.14 

250 

15.81 

103 


TABLE  OF  SQUARE   ROOTS. 

Nos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

251 

15.84 

301 

17.35 

351 

18.73 

401 

2002 

451 

21.24 

252 

1587 

302 

1738 

352 

18.76 

402 

2005 

452 

21.26 

253 

15.91 

303 

17.41 

353 

13.79 

403 

20.07 

453 

21.28 

254 

1594 

304 

1744 

354 

18.81 

404 

20  10 

454 

21.31 

255 

1597 

305 

17.46 

355 

18.84 

405 

20.12 

455 

21.33 

256 

1600 

306 

17.49 

356 

18.87 

406 

20.15 

456 

21  35 

257 

1603 

307 

17.52 

357 

18.89 

407 

80.17 

457 

21.33 

258 

16.06 

308 

17.55 

358 

1392 

408 

20.20 

458 

21  40 

259 

16.09 

309 

17.58 

359 

18.95 

409 

20.22 

459 

21  42 

260 

16.12 

310 

17.61 

360 

18.97 

410 

20.25 

460 

21.45 

261 

1616 

311 

1764 

361 

19.00 

411 

20.27 

461 

21.47 

262 

16  19 

312 

17.66 

362 

19.03 

412 

2030 

462 

21.49 

263 

16.22 

313 

1769 

363 

19.05 

413 

20.32 

463 

21  52 

264 

1625 

314 

17.72 

364 

19.08 

414 

20.35 

464 

21  54 

265 

16.28 

315 

17.75 

365 

19.10 

415 

20.37 

465 

21  55 

266 

1631 

316 

17.78 

366 

19.13 

416 

2040 

466 

21.59 

267 

1634 

3i7 

17.80 

3S7 

19.16 

417 

20.42 

467 

21.61 

268 

16.37 

318 

17.83 

368 

19.18 

418 

20.45 

468 

21.63 

269 

16.40 

319 

17.86 

369 

19.21 

419 

20.47 

469 

21.66 

270 

16.43 

320 

17.89 

370 

19.24 

420 

20.49 

470 

21.68 

271 

16.46 

321 

17.92 

371 

19.26 

421 

20.52 

471 

21.70 

272 

16.49 

322 

17.94 

372 

1929 

422 

20.54 

472 

21  73 

273 

16.52 

323 

17.97 

373 

19.31 

423 

20.57 

473 

21.75 

274 

1655 

324 

18.00 

374 

19.34 

424 

2059 

474 

21  77 

275 

16.58 

325 

18.03 

375 

19.36 

425 

20.62 

475 

21.79 

276 

16.61 

326 

18.06 

376 

19.39 

426 

2064 

476 

21.82 

277 

1664 

327 

18.08 

377 

19.42 

427 

20.66 

477 

21.84 

278 

16.67 

328 

18.11 

378 

19.44 

428 

20.69 

478 

21.86 

279 

16.70 

329 

18.14 

379 

19.47 

429 

20.71 

479 

21.89 

280 

16.73 

330 

18.17 

380 

19.49 

430 

20.74 

480 

21.91 

281 

15.76 

331 

18.19 

381 

19.52 

431 

20.76 

481 

21.93 

282 

13.79 

332 

1822 

382 

19.54 

432 

20.78 

482 

21.95 

283 

16  82 

333 

18.25 

383 

1957 

433 

20.81 

483 

21.98 

284 

1685 

334 

18.28 

384 

19.60 

434 

20.83 

484 

2200 

285 

16.88 

335 

18.30 

385 

19.62 

435 

20.86 

485 

22.02 

286 

1691 

336 

1833 

386 

19.65 

436 

20.88 

486 

22.05 

237 

1694 

337 

1836 

387 

19.67 

437 

20.90 

487 

22.07 

288 

16.97 

333 

18.38 

388 

19.70 

438 

20.93 

438 

2209 

289 

17.00 

339 

18.41 

389 

19.72 

439 

20.95 

489 

22.11 

290 

17.03 

340 

1844 

390 

19.75 

440 

2098 

490 

22.14 

291 

17.06 

341 

18.47 

391 

19.77 

441 

21.00 

491 

22.16 

292 

17.09 

342 

1849 

392 

19.80 

442 

21.02 

492 

22.18 

293 

17.12 

343 

18.52 

393 

19.82 

443 

21.05 

493 

22.20 

294 

17.15 

344 

18.55 

394 

19.85 

444 

21.07 

494 

22.23 

295 

17.18 

345 

18.57 

395 

19.87 

445 

21.10 

495 

22.25 

296 

17.20 

346 

18.60 

396 

19.90 

446 

21.12 

496 

22.27 

297 

17.23 

347 

18.63 

397 

19.92 

447 

21.14 

497 

22.29 

298 

17.26 

348 

13.65 

398 

19.95 

448 

21.17 

498 

22.32 

299 

17.29 

349 

18.68 

399 

19.97 

449 

21.19 

499 

22.34 

300 

17.32 

350 

18.71 

400 

20.00 

450 

21.21 

500 

22.36 

104 


TABLE  OF  SQUARE  ROOTS. 

Nos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

501 

22.38 

551 

23.47 

601 

24.52 

651 

25.51 

701 

26.43 

502 

22.41 

552 

23.49 

602 

24.54 

652 

25.53 

702 

26.50 

503 

22.43 

553 

23.52 

603 

24.56 

653 

25.55 

703 

26.51 

504 

22.45 

554 

23.54 

604 

24.58 

654 

25.57 

704 

26.53 

505 

22.47 

555 

23.56 

605 

24.60 

655 

25.59 

705 

2655 

506 

22.49 

556 

23.58 

606 

24.62 

656 

25.61 

706 

26.57 

507 

22.52 

557 

23.60 

607 

24.64 

657 

2563 

707 

2659 

508 

22.54 

553 

23.62 

608 

24.66 

658 

25.65 

708 

2661 

509 

2256 

559 

23.64 

609 

24.68 

659 

25.67 

709 

26.63 

510 

22.58 

560 

23.66 

610 

24.70 

660 

2569 

710 

2665 

511 

22.61 

561 

2369 

611 

24.72 

661 

25.71 

711 

2668 

512 

22.63 

562 

23.71 

612 

24.74 

662 

25.73 

712 

2668 

513 

2265 

563 

23.73 

613 

24.76 

663 

25.75 

713 

2670 

514 

22.67 

564 

23.75 

614 

24  78 

664 

25.77 

714 

26.72 

515 

22.69 

565 

23.77 

615 

24.80 

665  . 

25.79 

715 

26.74 

516 

2272 

566 

23.79 

616 

24.82 

666 

25.81 

716 

26.76 

517 

22  74 

567 

23.81 

617 

24.84 

667 

25.83 

717 

26.78 

518 

22.76 

568 

23  83 

618 

24.86 

668 

25.85 

718 

25.80 

519 

22.78 

569 

23.85 

619 

2488 

669 

25.87 

719 

26.81 

520 

22.80 

570 

23.87 

620 

2490 

670 

25.88 

720 

26.83 

521 

22  83 

571 

23.90 

621 

24.92 

671 

25.90 

721 

26.85 

522 

22.85 

572 

23.92 

622 

24.94 

672 

25.92 

722 

26.87 

523 

22  87 

573 

23.94 

623 

24.96 

673 

2594 

723 

2689 

524 

22.89 

574 

2396 

624 

24.98 

674 

25.96 

724 

26.91 

525 

22.91 

575 

23.98 

625 

25.00 

675 

25.98 

725 

26.93 

526 

22.93 

576 

24.00 

626 

25.02 

676 

26.00 

726 

26.94 

527 

22.96 

577 

24.02 

627 

25.04 

677 

26.02 

727 

26.96 

528 

22.98 

578 

2404 

628 

25.06 

678 

2604 

728 

26.98  • 

529 

23.00 

579 

24.06 

629 

2508 

679 

26.06 

729 

27.00 

530 

2302 

580 

24.08 

630 

25.10 

680 

2608 

730 

27.02 

531 

23.04 

581 

24.10 

631 

25.12 

681 

26  10 

731 

27.04 

532 

23.07 

582 

24.12 

632 

25.14 

682 

2612 

732 

27.06 

533 

23.09 

583 

24.15 

633 

25.16 

683 

26.13 

733 

27.07 

534 

23.11 

584 

24.17 

634 

25.18 

684 

26  15 

734 

2709 

535 

23.13 

585 

24.19 

635 

25.20 

685 

26.17 

735 

2711 

536 

23.15 

586 

24.21 

636 

25.22 

686 

26.19 

736 

27.13 

537 

2317 

537 

24.23 

637 

25.24 

687 

2621 

737 

27.15 

533 

23.19 

588 

24.25 

633 

2526 

688 

2623 

738 

27.17 

539 

23.22 

589 

24.27 

639 

2528 

689 

26.25 

739 

2718 

540 

23.24 

590 

24.29 

.640 

2530 

690 

26.27 

740 

27.20 

541 

23.26 

591 

24.31 

641 

25.32 

691 

2629 

741 

27.22 

542 

23.28 

592 

24.33 

642 

'25.34 

692 

2631 

742 

27.24 

543 

23.30 

593 

24.35 

643 

25.36 

693 

2632 

743 

27.26 

544 

2332 

594 

24  37 

644 

2538 

694 

26.34 

744 

27.28 

545 

2335 

595 

24.39 

645 

25.40 

695 

26-36 

745 

27.29 

546 

2337 

596 

24.41 

646 

2542 

696 

26.38 

746 

27.31 

547 

2339 

597 

2443 

647 

2544 

697 

2640 

747 

27.33 

548 

2341 

598 

24.45 

648 

25.46 

698 

26.42 

748 

2735 

549 

23.43 

599 

24.47 

649 

2548 

699 

2644 

749 

2737 

550 

23.45 

600 

24  49 

'650 

2550 

700 

26.46 

750 

27.39 

105 


TABLE  OF  SQUARE  ROOTS. 

I* 

Roots 

Nos. 

Roots 

Nos. 

R.MltS 

Sos. 

Roots 

Nos. 

Roots 

751 

27.40 

801 

28.30 

851 

29.17 

901 

30.02 

951 

30.84 

752 

27.42 

802 

2832 

852 

29.19 

902 

30.03 

952 

30.85 

753 

27.44 

803 

28.34 

853 

29.21 

903 

30.05 

953 

30.87 

754 

27.46 

804 

28.35 

854 

29.22 

904 

30.07 

954 

30.89 

755 

27.48 

805 

28.37 

855 

29.24 

905 

30.08 

955 

30.90 

756 

27.50 

806 

28.39 

856 

29.26 

906 

30.10 

956 

30.92 

757 

27.51 

807 

28.41 

857 

29.27 

907 

30.12 

957 

30.94 

758 

27.53 

808 

28.43 

858 

29.29 

908 

30.13 

958 

30.95 

759 

27.55 

809 

28.44 

859 

29.31 

909 

30.15 

959 

30.97 

760 

27.57 

810 

28.46 

860 

29.33 

910 

30.17 

960 

30.98 

761 

27.59 

811 

28.48 

861 

29.34 

911 

30.18 

961 

31.00 

762 

27.60 

812 

28.50 

862 

2936 

912 

30.20 

962 

31.02 

763 

2762 

813 

28.51 

863 

2938 

913 

30.22 

963 

31.03 

764 

27.64 

814 

28.53 

864 

29.39 

914 

30.23 

964 

31.05 

765 

27.66 

815 

28.55 

865 

29.41 

915 

30.25 

965 

31.06 

766 

27.68 

816 

28.57 

866 

29.43 

916 

30.27 

966 

31.08 

767 

27.69 

817 

28.58 

867 

29.44 

917 

30.28 

967 

31.10 

768 

27.71 

818 

2860 

868 

29.46 

918 

30.30 

968 

31.11 

769 

27.73 

819 

28.62 

869 

29.48 

919 

30.32 

969 

31.13 

770 

27.75 

820 

28.64 

870 

29.50 

920 

30.33 

970 

31.14 

771 

27.77 

821 

28.65 

871 

29.51 

921 

30.35 

971 

31.16 

772 

27  78 

822 

28.67 

872 

29.53 

922 

30.36 

972 

31.18 

773 

27.80 

823 

28.69 

873 

29.55 

923 

30.38 

973 

31.19 

774 

27.82 

824 

28.71 

874 

29.56 

924 

30.40 

974 

31.21 

775 

27.84 

825 

28.72 

875 

29.58 

925 

30  A  1 

975 

31.22 

776 

27.86 

826 

28.74 

876 

29.60 

926 

30.43 

976 

31.24 

777 

27.87 

827 

28.76 

877 

29.61 

927 

30.45 

977 

31.26 

•778 

27.89 

828 

28.77 

878 

29.63 

928 

30.46 

978 

31.27 

V79 

27.91 

829 

28.79 

879 

29.65 

929 

30.48 

979 

31.29 

780 

27.93 

830 

28.81 

880 

29.66 

930 

30.50 

980 

31.30 

781 

27.95 

831 

28.83 

881 

29.6° 

931 

30.51 

981 

31.32 

782 

27.96 

832 

28.84 

882 

29.70 

932 

3053 

982 

31.34 

783 

27.98 

833 

28.86 

883 

29.72 

933 

30.55 

983 

31.35 

784 

2800 

834 

28.88 

884 

29.73 

934 

30.56 

984 

31.37 

785 

28.02 

835 

28.90 

885 

29.75 

935 

30.58 

985 

31.38 

786 

28.04 

836 

28.91 

886 

29.77 

936 

30.59 

986 

31.40 

787 

28.05 

837 

28.93 

887 

29.78 

937 

30.61 

987 

31.42 

788 

28.07 

838 

28.95 

888 

29.80 

938 

30.63 

988 

31.43 

789 

28.09 

839 

2897 

889 

29.82 

939 

3064 

989 

31.45 

790 

28.11 

840 

28.98 

890 

29.83 

940 

30.66 

990 

31.46 

791 

28.12 

841 

29.00 

891 

29.85 

941 

30.68 

991 

31.48 

792 

28.14 

842 

29.02 

892 

29.87 

942 

30.69 

992 

31.50 

793 

28.16 

843 

29.03 

893 

29.88 

943 

30.71 

993 

31.51 

794 

28.18 

844 

29.05 

894 

29.90 

944 

30.72 

994 

31.53 

795 

28.20 

845 

29.07 

895 

29.92 

945 

30.74 

995 

31.54 

796 

28.21 

846 

29.09 

896 

2993 

946 

30.76 

996 

3156 

797 

28.23 

847 

29.10 

897 

29.95 

947 

30.77 

997 

31.58 

798 

28.25 

848 

29.12 

898 

29.97 

948 

3079 

998 

31.59 

799 

28.27 

849 

29.14 

899 

29.98 

949 

3081 

999 

31.61 

800 

28.28 

850 

29.15 

900 

30.00 

950 

30.82 

1000 

31.62 

106 


TABLE  OF  SQUARE  ROOTS. 

to. 

Roots 

Nos. 

Root* 

Sos. 

Roots 

Nos. 

Rjoik 

Nos. 

Roots 

1001 

31.64 

1051 

32.42 

1101 

33.18 

1151 

33.93 

1201 

34.66 

1002 

31.65 

1052 

3243 

1102 

33.20 

1152 

33.94 

1202 

34.67 

1003 

31.67 

1053 

32.45 

1103 

3321 

1153 

33.96 

1203 

34.68 

1004 

31.69 

1054 

32.47 

1104 

33.23 

1154 

33.97 

1204 

34.70 

1005 

31.70 

1055 

32.48 

1105 

33.24 

1155 

33.99 

1205 

34.71 

1006 

31.72 

1056 

32.50 

1106 

33.26 

1156 

34.00 

1206 

34.73 

1007 

31.73 

1057 

32.51 

1107 

33.27 

1157 

34.01 

1207 

34.74 

1008 

31.75 

1058 

32.53 

1108 

33.29 

1158 

34.03 

1208 

34.76 

1009 

31.76 

1059 

32.54 

1109 

33.30 

1159 

34.04 

1209 

34.77 

1010 

31.78 

1060 

32.56 

1110 

33.32 

1160 

•34.06 

1210 

34.79 

1011 

31.80 

1061 

32.57 

1111 

33.33 

1161 

34.07 

1211 

34.80 

1012 

31.81 

1062 

32.59 

1112 

33.35 

1162 

34.09 

1212 

34.81 

1013 

31.83 

1063 

32.60 

1113 

33.36 

1163 

34.10 

1213 

34.83 

1014 

31.84 

1064 

32.62 

1114 

33.38 

1164 

34.12 

1214 

34.84 

1015 

31.86 

1065 

32.63 

1115 

33.39 

1165 

34.13 

1215 

34.86 

1016 

31.87 

1066 

3265 

1116 

33.41 

1166 

34.15 

1216 

34.87 

1017 

31.89 

1067 

32.66 

1117 

33.42 

1167 

34.16 

1217 

34.89 

1018 

31.91 

1068 

3268 

1118 

33.44 

1168 

34.18 

1218 

34.90 

1019 

31.92 

1069 

32.70 

1119 

33.45 

1169 

34  19 

1219 

34.91 

1020 

31.94 

1070 

32.71 

1120 

33.47 

1170 

34.21 

1220 

34.93 

1021 

31.95 

1071 

32.73 

1121 

33.48 

1171 

34.22 

1221 

34.94 

1022 

31  97 

1072 

32.74 

1122 

33.50 

1172 

34.23 

1222 

3496 

1023 

31.98 

1073 

3276 

1123 

33.51 

1173 

34.25 

1223 

34.97 

•   1024 

32.00 

1074 

32.77 

1124 

33.53 

1174 

34.26 

1224 

34.99 

1025 

32.02 

1075 

32.79 

1125 

33.54 

1175 

34.28 

1225 

35.00 

1026 

32.03 

1076 

32.80 

1126 

33.56 

1176 

34.29 

1226 

35.01 

1027 

32.05 

1077 

32.82 

1127 

33.57 

1177 

34.31 

1227 

3503 

1028 

32.06 

1078 

32.83 

1128 

33.59 

1178 

34.32 

1228 

35.04 

1029 

32.08 

1079 

32.85 

1129 

33.60 

1179 

34.34 

1229 

35.06 

1030 

32.09 

1080 

32.86 

1130 

33.62 

1180 

34.35 

1230 

35.07 

1031 

32.11 

1081 

32.88 

1131 

33.63 

1181 

34.37 

1231 

35.09 

1032 

32.12 

1082 

32.89 

1132 

33.65 

1182 

34.38 

1232 

35.10 

1033 

32.14 

1083 

32.91 

1133 

33.66 

1183 

34.39 

1233 

35.11 

1034 

32.16 

1084 

32.92 

1134 

33.67 

1184 

34.41 

1234 

35.13 

1035 

32.17 

1085 

32.94 

1135 

33.69 

1185 

34.42 

1235 

35.14 

1036 

32.19 

1086 

32.95 

1136 

33.70 

1186 

34.44 

1236 

35.16 

1037 

32.20 

1087 

32.97 

1137 

33.72 

1187 

34.45 

1237 

35.17 

1038 

32.22 

1088 

32.98 

1138 

33.73 

1188 

34.47 

1238 

35.19 

1039 

32.23 

1089 

3300 

1139 

33.75 

1189 

3448 

1239 

35.20 

'1040 

32.25 

1090 

33.02 

1140 

33.76 

1190 

34.50 

1240 

35.21 

1041 

32.26 

1091 

33.03 

1141 

33.78 

1191 

34.51 

1241 

35.23 

1042 

32.28 

1092 

33.05 

1142 

3379 

1192 

34.53 

1242 

35.24 

1043 

32.30 

1093 

33.06 

1143 

33.81 

1193 

34.54 

1243 

35.26 

1044 

32.31 

1094 

33.08 

1144 

33.82 

1194 

34.55 

1244 

35.27 

1045 

32.33 

1095 

33.09 

1145 

33.84 

1195 

34.57 

1245 

35.28 

1046 

32.34 

1096 

33.11 

1146 

33.85 

1196 

34.58 

1246 

3530 

1047 

32.36 

1097 

33.12 

1147 

33.87 

1197 

34.60 

1247 

35.31 

1048 

32.37 

1098 

33.14 

1148 

3388 

1198 

34.61 

1248 

35.33 

1049 

32.39 

1099 

33.15 

1149 

3390 

1199 

3463 

1249 

35.34 

1050 

32.40 

1100 

33  17 

1150 

33.91 

1200 

34.61 

1250 

35.36 

107 


TABLE  OF  SQUARE  ROOTS 

Hos. 

Roots 

N<H. 

Roots 

1* 

Roots 

Nos. 

Roots 

Nos. 

Roots 

1251 

35.37 

1301 

36.07 

1351 

36.76 

1401 

37.43 

1451 

38.09 

1252 

3538 

1302 

3608 

1352 

36.77 

1402 

37.44 

1452 

38.11 

1253 

35.40 

1303 

36.10 

1353 

36.78 

1403 

3746 

1453 

38.12 

1254 

35.41 

1304 

36.11 

1354 

26  80 

1404 

3747 

1454 

3813 

1255 

35.43 

1305 

36.12 

]355 

36.81 

1405 

37.48 

1455 

38.14 

1256 

35.44 

1306 

36.14 

1356 

3682 

1406 

3750 

1456 

38.16 

1257 

3545 

1307 

36.15 

1357 

36.84 

1*07 

37.51 

1457 

38.17 

1258 

35.47 

1308 

35.17 

1358 

36  85 

1403 

37.52 

1458 

38.13 

1259 

35.48 

1309 

36.18 

1359 

3686 

1409 

3751 

1459 

3820 

1260 

3550 

1310 

36.19 

1360 

36.38 

1410 

37.55 

1460 

38.21 

1261 

35.51 

1311 

36.21 

1361 

3689 

1411 

37.56 

1461 

38.22 

1262 

35.52 

1312 

36.22 

1362 

36  91 

1412 

37.58 

1462 

3324 

1263 

35.54 

1313 

36.24 

1363 

36  92 

1413 

37.59 

1463 

38.25 

1264 

3555 

1314 

36.25 

1364 

36.93 

1414 

37.60 

1464 

38.26 

1265 

3557 

1315 

36.26 

1365 

36.95 

1415 

3762 

1465 

38.28 

1266 

35.58 

1316 

3623 

1366 

36.96 

1416 

37.63 

1466 

38.29 

1267 

3559 

1317 

36.29 

1367 

36.97 

1417 

37.64 

1467 

38.30 

1268 

35.61 

1318 

36.30 

1363 

3699 

1418 

37.66 

1468 

38.31 

1269 

3562 

1319 

36.32 

1369 

37.00 

1419 

3767 

1469 

38.33 

1270 

35.64 

1320 

36.33 

1370 

37.01 

1420 

3768 

1470 

38.34 

1271 

3565 

1321 

3635 

1371 

37.03 

1421 

37.70 

1471 

38.35 

1272 

35.67 

1322 

36.36 

1372 

27.04 

1422 

37.71 

1472 

3837 

1273 

35.68 

1323 

36.37 

1373 

37.05 

1423 

37.72 

1473 

38.38 

1274 

35.69 

1324 

36.39 

1374 

3707 

1424 

37.74 

1474 

38.39 

1275 

35.71 

1325 

36.40 

1375 

37.08 

1425 

37.75 

1475 

38.41 

1276 

35.72 

1326 

36.41 

1376 

37.09 

1426 

37.76 

1476 

38.42 

1277 

35.74 

1327 

36.43 

1377 

37.11 

1427 

37.78 

1477 

3843 

1278 

35.75 

1328 

36.44 

1378 

37.12 

1428 

37.79 

1478 

33.44 

1279 

35.76 

1329 

36.46 

1379 

37.13 

1429 

3780 

1479 

3846 

1280 

35.78 

1330 

36.47 

1380 

37.15 

1430 

37.82 

1480 

3847 

1281 

35.79 

1331 

36.48 

1381 

37.16 

1131 

37.83 

1481 

3843 

1282 

3581 

1332 

36.50 

1382 

37.18 

1432 

37.84 

1482 

33.50 

1283 

35  82 

1333 

36.51 

1383 

37.19 

1433 

37.85 

1483 

3351 

1234 

35.83 

1334 

3652 

1384 

37.20 

1434 

37.87 

1484 

3352 

1285 

35.85 

1335 

36.54 

1385 

37.22 

1435 

37.88 

1485 

38.54 

1286 

35.86 

1336 

36.55 

1386 

37.23 

1436 

37.89 

1486 

3355 

1287 

35.87 

1337 

36.57 

1387 

37.24 

1437 

37.91 

1487 

3856 

1288 

35.89 

1333 

36.58 

1388 

37.26 

1438 

3792 

1483 

33.57 

1289 

3590 

1339 

36.59 

1389 

3727 

1439 

3793 

1489 

38.59 

1290 

35.92 

1340 

36.61 

1390 

37.28 

1440 

3795 

1490 

38.60 

1291 

3593 

1341 

36.62 

1391 

37.30 

1441 

3796 

1491 

3361 

1292 

35.94 

1342 

3663 

1392 

37.31 

1442 

3797 

1492 

3363 

1293 

3596 

1343 

3665 

1393 

3732 

1443 

37.99 

1493 

38.64 

1294 

3597 

1344 

36.66 

1394 

37.34 

1444 

3300 

1494 

38.65 

1295 

35.99 

1345 

36.67 

1395 

37.35 

1445 

38.01 

1495 

38.67 

1296 

36.00 

1346 

3669 

1396 

37.36 

1446 

3803 

1496 

3868 

1297 

36.01 

1347 

36.70 

1397 

37.38 

1447 

3804 

1497 

38.69 

1298 

36.03 

1348 

36.72 

1398 

3739 

1448 

38.05 

1498 

38  70 

1299 

36.04 

1349 

3673 

1399 

3740 

1449 

3807 

1499 

38.72 

1300 

36.06 

1350 

36  74 

1400 

37.42 

1450 

33  08  I  1500 

38.73 

108 


TABLE  OF  SQUARE  ROOTS. 

Nos. 

Rooti 

Nos. 

Roots 

Not. 

Rjoti 

Nos. 

Roots 

Nos. 

Roots 

1501 

38.74 

1551 

39.38 

1601 

40.01 

1651 

40.63 

1701 

41.24 

1502 

3876 

1552 

39.40 

1602 

40.02 

1652 

40.64 

1702 

41.26 

1503 

38.77 

1553 

39.41 

1603 

40.04 

1653 

40.66 

1703 

41.27 

1504 

38.78 

1554 

39.42 

1604 

40.05 

1654 

40.67 

1704 

41.28 

1505 

38.7S 

1555 

39.43 

1605 

40.06 

1655 

40.68 

1705 

41.29 

1506 

38.81 

1556 

39.45 

1606 

40.07 

1656 

40.69 

1706 

41.30 

1507 

38.82 

1557 

39.46 

1607 

40.09 

1657 

40.71 

1707 

41.32 

1508 

38.83 

1558 

39.47 

1608 

40.10 

1658 

40.72 

1708 

41.33 

1509 

38.85 

1559 

39.48 

1609 

40.11 

1659 

40.73 

1709 

41.34 

1510 

38.96 

1560 

39.50 

1610 

40.12 

1660 

40.74 

1710 

41.35 

1511 

38.87 

1561 

39.51 

1611 

40.14 

1661 

40.76 

1711 

41.36 

1512 

38.88 

1562 

39.52 

1612 

40.15 

1662 

40.77 

1712 

41.38 

1513 

38.90 

1563 

39.53 

1613 

40.16 

1663 

10.78 

1713 

41.39 

1514 

38.91 

1564 

39.55 

1614 

40.17 

1564 

40.79 

1714 

41.40 

1515 

38.92 

1565 

39.56 

1615 

40.19 

1665 

40.80 

1715 

41.41 

1516 

38.94 

1566 

39.57 

1616 

40.20 

1666 

40.82 

1716 

41.42 

1517 

38.95 

1567 

39.59 

1617 

40.21 

1667 

40.83 

1717 

41.44 

1518 

38.96 

1568 

39.60 

1618 

4022 

1668 

40.84 

1718 

41.45 

1519 

38.97 

1569 

39.61 

1619 

4024 

1669 

40.85 

1719 

41.46 

1520 

38.99 

1570 

39.62 

1620 

40.25 

1670 

40.87 

1720 

41.47 

1521 

39.00 

1571 

39.64 

1621 

40.26 

1671 

40.88 

1721 

41.48 

1522 

39.01 

1572 

39.65 

1622 

40.27 

1672 

4089 

1722 

41.50 

1523 

3903 

1573 

39.66 

1623 

40.29 

1673 

40.90 

1723 

41.51 

1524 

39.04 

1574 

39.67 

1624 

40.30 

1674 

40.91 

1724 

41.52 

1525 

39.05 

1575 

39.69 

1625 

40.31 

1675 

40.93 

1725 

41.53 

1526 

39.06 

1576 

39.70 

1626 

40.32 

1676 

40.94 

1726 

41.55 

1527 

39.08 

1577 

39.71 

1627 

40.34 

1677 

40.95 

1727 

41.56 

1528 

39.09 

1578 

39.72 

1628 

40.35 

1678 

40.96 

1728 

41.57 

1529 

39.10 

1579 

39.74 

1629 

40.36 

1679 

40.98 

1729 

41.58 

1530 

39.12 

1580 

39.75 

1630 

40.37 

1680 

40.99 

1730 

4159 

1531 

39.13 

1581 

39.76 

1631 

40.39 

1681 

41.00 

1731 

41.61 

1532 

39.14 

1582 

39.77 

1632 

40.40 

1682 

41.01 

1732 

41.62 

1533 

39.15 

1583 

39.79 

1633 

40.41 

1683 

41.02 

1733 

41.63 

1534 

39.17 

1584 

39.80 

1634 

40.42 

1684 

41.04 

1734 

4164 

1535 

39.18 

1585 

39.81 

1635 

40.44 

1685 

41.05 

1735 

41.65 

1536 

39.19 

1586 

39.82 

1636 

40.45 

1686 

41.06 

1736 

41.67 

1537 

39.20 

1587 

39.84 

1637 

40.46 

1687 

41.07 

1737 

41.68 

1538 

39.22 

1588 

39.85 

1638 

40.47 

1688 

41.09 

1738 

41.69 

1539 

3923 

1589 

39.86 

1639 

4048 

1689 

41.10 

1739 

41.70 

1540 

39.24 

1590 

39.87 

1640 

40.50 

1690 

41.11 

1740 

41.71 

1541 

39.26 

1591 

39.89 

1641 

40.51" 

1691 

41.12 

1741 

41.73 

1542 

39.27 

1592 

39.90 

1642 

40.52 

1692 

41.13 

1742 

41.74 

1543 

39.28 

1593 

39.91 

1643 

40.53 

1693 

41.15 

1743 

41.75 

1544 

39.29 

1594 

39.92 

1644 

40.55 

1694 

41.16 

1744 

41.76 

1545 

39.31 

1595 

39.94 

1645 

40.56 

1695 

41.17 

1745 

41.77 

1546 

39.32 

1596 

39.95 

1646 

40.57 

1696 

41.18 

1746 

41.79 

1547 

39.33 

1597 

3996 

1647 

40.58 

1697 

41.19 

1747 

4180 

1548 

39.34 

1598 

3997 

1648 

40.60 

1698 

41.21 

1648 

41.81 

1549 

39.36 

1599 

39.99 

1649 

40.61 

1699 

41.22 

1749 

41.82 

1550 

39.37 

1600 

40.00 

1650 

40.62 

1700 

41.23 

1750 

41.83 

109 


TABLE  OF  SQUARE  ROOTS. 

Nos. 

Rooti 

Xos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

1751 

41.85 

1801 

42.44 

1851 

43.02 

1901 

43.60 

1951 

44.17 

1752 

41.86 

1802 

42.45 

1852 

43.03 

1902 

43.61 

1952 

44.18 

1753 

41.87 

1803 

42.46 

1853 

43.05 

1903 

4362 

1953 

44.19 

1754 

41.88 

1804 

42.47 

1854 

43.06 

1904 

4363 

1954 

44.20 

1755 

41.89 

1805 

42.49 

1855 

43.07 

1905 

43.65 

1955 

44.22 

1756 

41.90 

1806 

42.50 

1856 

43.08 

1906 

43.66 

1956 

44.23 

1757 

4192 

1807 

42.51 

1857 

4309 

1907 

43.67 

1957 

44  24 

1758 

41.93 

1808 

4252 

1858 

43.10 

1908 

43.68 

1958 

44.25 

1759 

41  94 

1809 

42.53 

1859 

43.12 

1909 

43.69 

1959 

44.26 

1760 

41.95 

1810 

42.54 

1860 

4313 

1910 

43.70 

1960 

44.27 

1761 

41.96 

1811 

4256 

1861 

43  14 

1911 

43.71 

1961 

44.28 

1762 

41.98 

1812 

4257 

1862 

4315 

1912 

43.73 

1962 

44.29 

1763 

41  99 

1813 

4258 

1863 

43.16 

1913 

43.74 

1963 

44.31 

1764 

42.00 

1814 

42.59 

1864 

43.17 

1914 

4375 

1964 

44.32 

1765 

42.01 

1815 

42.60 

1865 

43.19 

1915 

43.76 

1965 

44.33 

1766 

42.02 

1816 

42.61 

1866 

43.20 

1916 

43.77 

1966 

44.34 

1767 

4204 

1817 

42.63 

1867 

43.21 

1917 

43.78 

1967 

44.35 

1768 

42.05 

1818 

42.64 

1868 

43.22 

1918 

43.79 

1968 

44.36 

1769 

42.06 

1819 

42.65 

1869 

43.23 

1919 

4381 

1969 

44.37 

1770 

42.07 

1820 

42.66 

1870 

43.24 

1920 

4382 

1970 

44.38 

1771 

42.08 

1821 

42.67 

1871 

43.26 

1921 

43.83 

1971 

44.40 

1772 

42.10 

1822 

42.68 

1872 

43.27 

1922 

43.84 

1972 

44.41 

1773 

42.11 

1823 

42.70 

1873 

43.28 

1923 

43.85 

1973 

44.42 

1774 

42.12 

1824 

42.71 

1874 

4329 

1924 

43.86 

1974 

44.43 

1775 

42.13 

1825 

42.72 

1875 

43.30 

1925 

43.87 

1975 

44.44 

1776 

42.14 

1826 

42.73 

1876 

43.31 

1926 

43.89 

1976 

44.45 

1777 

42.15 

1827 

42.74 

1877 

43.32 

1927 

43.90 

1977 

44.46 

1778 

42.17 

1828 

4276 

1878 

43.34 

1928 

43.91 

1978 

44.47 

1779 

42.18 

1829 

42.77 

1879 

43.35 

1929 

4392 

1979 

44.49 

1780 

42.19 

1830 

42.78 

1880 

43.36 

1930 

43.93 

1980 

44.50 

1781 

42.20 

1831 

42.79 

1881 

43.37 

1931 

43.94 

1981 

44  51 

1782 

42.21 

1832 

42.80 

1882 

43.38 

1932 

43.95 

1982 

44.52 

1783 

4223 

1833 

42.81 

1883 

43.39 

1933 

43.97 

1983 

44.53 

1784 

42.24 

1834 

42.83 

1884 

4341 

1934 

43.98 

1984 

44  54 

1785 

42.25 

1835 

42.84 

1885 

43.42 

1935 

43.99 

1985 

44  55 

1786 

4226 

1836 

42.85 

1886 

43.43 

1936 

44.00 

1986 

44.56 

1787 

4227 

1837 

42.86 

1887 

43.44 

1937 

44.01 

1987 

44  58 

1788 

42.28 

1838 

42.87 

1888 

43.45 

1938 

4402 

1988 

44  59 

1789 

4230 

1839 

42.88 

1889 

4346 

1939 

44.03 

1989 

44.60 

1790 

42.31 

1840 

42.90 

1890 

43.47 

1940 

4405 

1990 

44.61 

1791 

42.32 

1841 

42.91 

'1891 

43.49 

1941 

44.06 

1991 

44.62 

1792 

42.33 

1842 

4292 

1892 

43.50 

1942 

44.07 

1992 

44  63 

1793 

42.34 

1843 

42.93 

1893 

43.51 

1943 

44.08 

1993 

44.64 

1794 

42.36 

1844 

42.94 

1894 

43.52 

1944 

44.09 

1994 

44.65 

1795 

4237 

1845 

42.95 

1895 

43.53 

1945 

44.10 

1995 

44.67 

1796 

42.38 

1846 

42.97 

1896 

43.54 

1946 

44.11 

1996 

44.68 

1797 

42.39 

1847 

4298 

1897 

43.55 

1947 

44.12 

1997 

44.69 

1798 

4240 

1848 

42.99 

1898 

4357 

1948 

44.14 

1998 

44.70 

1799 

42.41 

1849 

43.00 

1899 

43.58 

1949 

44.15 

1999 

44.71 

1800 

42.43 

1850 

43.01 

1900 

43.59 

1950 

44.16 

2000 

44.72 

TABLE  OF  SQUARE  ROOTS 

Nos. 

Roots 

Nos. 

Rjots 

Nos. 

Roots 

Nos. 

Roots 

Nos. 

Roots 

2001 

44.73 

2051 

45.29 

2101 

45.84 

2151 

46.38 

2201 

4692 

2002 

44.74 

2052 

45.30 

2102 

45.85 

2152 

4639 

2202 

46.83 

2003 

44.75 

2053 

4531 

2103 

45.86 

2153 

46.40 

2203 

46.94 

2004 

44.77 

2054 

45.32 

2104 

4587 

2154 

46.41 

2204 

4695 

2005 

44.78 

2055 

45.33 

2105 

45.88 

2155 

46.42 

2205 

46.96 

2006 

44.79 

2056 

45.34 

2106 

45.89 

2156 

46.43 

2206 

4697 

2007 

44.80 

2057 

45.35 

2107 

45.90 

2157 

46.44 

2207 

46.98 

2008 

44.81 

2058 

4537 

2108 

45.91 

2158 

46.45 

2208 

46.99 

2009 

44.82 

2059 

45.38 

2109 

45.92 

2159 

46.47 

2209 

47.00 

2010 

44.83 

2050 

4539 

2110 

45.93 

2160 

46.48 

2210 

47.01 

2011 

44.84 

2061 

45.40 

2111 

4595 

2161 

46.49 

2211 

47.02 

2012 

44.85 

2062 

45.41 

2112 

4596 

2162 

4650 

2212 

47.03 

2013 

44.87 

2063 

45.42 

2113 

45.97 

2163 

46.51 

2213 

47.04 

2014 

44.88 

2064 

45.43 

2114 

45.98 

2164 

46.52 

2214 

47.05 

2015 

44.89 

2065 

45.44 

2115 

45.99 

2165 

46.53 

2215 

47.06 

2016 

44.90 

2066 

45.45 

2116 

46.00 

2166 

46.54 

2216 

47.07 

2017 

44.91 

2067 

45.46 

2117 

46.01 

2167 

4655 

2217 

47.09 

2018 

44.92 

2068 

45.48 

2118 

46.02 

2168 

4656 

2218 

47.10 

2019 

44.93 

2069 

45.49 

2119 

46.03 

2169 

4657 

2219 

47.11 

2020 

44.94 

2070 

45.50 

2120 

46.04 

2170 

46.58 

2220 

47-12 

2021 

4495 

2071 

45.51 

2121 

46.05 

2171 

46.59 

2221 

4713 

2022 

44.97 

20^2 

4552 

2122 

46.07 

2172 

4660 

2222 

47.14 

2023 

44.98 

2073 

4^.o3 

2i23 

4608 

2173 

46.62 

2223 

47.15 

2024 

44.99 

2074 

45.54 

2i24 

46.09 

2174 

46.63 

2224 

47.16 

2025 

45.00 

2075 

45.55 

2125 

46.10 

2175 

46.64 

2225 

47.17 

2026 

4501 

2076 

45.56 

2126 

46.11 

2176 

4665 

2226 

47  18 

2027 

45.02 

2077 

45.57 

2127 

46.12 

2177 

46.66 

2227 

47.19 

2028 

45.03 

2078 

45.59 

2128 

46.13 

2178 

46.67 

2228 

47.20 

2029 

45.04 

2079 

4560 

2129 

46.14 

2179 

46.68 

2229 

47.21 

2030 

45.06 

2080 

45.61 

2130 

46.15 

2180 

46.69 

2230 

47.22 

2031 

45.07 

2081 

4562 

2131 

46.16 

2181 

46.70 

2231 

47.23 

2032 

45.08 

2082 

45.63 

2132 

46.17 

2182 

46.71 

2232 

47.24 

2033 

4509 

2033 

45.64 

2133 

46.18 

2183 

.46.72 

2233 

47.25 

2034 

45.10 

2084 

45.65 

2134 

46.19 

2184 

46.73 

2234 

47.26 

2035 

45.11 

2085 

45.66 

2135 

46.21 

2185 

46.74 

2235 

47.23 

2036 

45.12 

2086 

45.67 

2136 

46.22 

2186 

46.76 

2236 

47.29 

2037 

45.13 

2087 

45.68 

2137 

46.23 

2187 

46.77 

2237 

47.30 

2033 

45.14 

2088 

45.69 

2133 

46.24 

2188 

46  78 

2238 

47.31 

2039 

45.16 

2089 

45.71 

2139 

46.25 

2189 

46.79 

2239 

47.32 

2040 

45.17 

2090 

45.72 

2140 

4626 

2190 

46.80 

2240 

47.33 

2041 

45.18 

2091 

45.73 

2141 

46.27 

2191 

46.81 

2241 

47.34 

2042 

4519 

2092 

4574 

2142 

4628 

2192 

4682 

2242 

47.35 

2043 

45.20 

2093 

45.75 

2143 

46.29 

2193 

46.83 

2243 

47.36 

2044 

45.21 

2094 

45.76 

2144 

46.30 

2194 

46.84 

2244 

47.37 

2045 

45.22 

2095 

45.77 

2145 

46.31 

2195 

46.85 

2245 

47.38 

2046 

45.23 

2096 

45.78 

2146 

4632 

2196 

46.86 

2246 

47.39 

2047 

45.24 

2097 

45.79 

2147 

46.34 

2197 

46.87 

2247 

47  40 

2048 

45.25 

2098 

45.80 

2148 

46.35 

2198 

46.88 

2248 

4741 

2049 

4527 

2099 

45.82 

2149 

46.36 

2199 

46.89 

2249 

47  42 

2050 

45.28 

2100 

45.83 

2150 

46.37  ' 

2200 

45.90 

2250 

47.43 

SWI  NG    BRIDGES. 


THREE    POINTS     OF     SUPPORT. 
TWO   EQUAL  ARMS. 


REACTIONS,  SHEARING  STRESSES  AND 
BENDING  MOMENTS. 


Single  I/Dads,         -        -        -      pages  113  to  128. 
Symmetrical  Loads,          -  "       12810142. 


The  following  Tables  are  based  on  the  assumption 
of  a  panel  load  and  panel  length  of  unity.  The  actual 
shear  will,  therefore,  be  obtained  by  multiplying  the  act- 
ual panel  load  by  the  tabular  shear,  and  the  actual  mo- 
ment will  be  found  by  multiplying  the  actual  panel  load 
by  the  actual  panel  length  and  by  the  proper  tabular 
coefficient. 

If  the  chords  are  not  parallel  the  web  stresses  may 
be  obtained  by  the  method  of  moments,  or  by  a  combina- 
tion of  the  method  of  moments  and  graphics. 

As  the  coefficients  are  based  on  unity  both  for  load 
and  panel  length,  the  tables  are  applicable  to  any  system 
of  measurement  and  apply  with  equal  facility  to  pounds, 
tons  or  kilogrammes  and  feet,  inches  or  metres. 

The  coefficients  are  derived  from  the  formulae  of  the 
"Theorem  of  Three  Moments"  and  are  therefore  appli- 
cable for  the  conditions  upon  which  the  theory  was 
developed. 


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SWING      BRIDGES. 


FOUR  POINTS  OF  SUPPORT. 
PARTIAL  CONTINUITY. 
TWO  EQUAL  ARMS. 

SYMMETRICAL  LOADS. 


REACTIONS,  SHEARING  STRESSES  AND 
BENDING  MOMENTS. 


The  following  tables  are  based  on  the  assumption  of 
a  panel  load  and  panel  length  of  unity.  The  actual 
shear  will,  therefore,  be  obtained  by  multiplying  the 
actual  panel  load  by  the  tabular  shear,  and  the  actual 
moment  will  be  found  by  multiplying  the  actual  panel 
load  by  the  actual  panel  length  and  by  the  proper  tabu- 
lar coefficient. 

If  the  chords  are  not  parallel  the  web  stresses  may 
be  obtained  by  the  method  of  moments,  or  by  a  combin- 
ation of  the  method  of  moments  and  graphics. 

If  the  length  of  the  center  panel  should  differ  to 
some  extent  from  the  others,  the  tabular  coefficient  will 
not  be  sensibly  changed. 

EXAMPLE. 

For  shear  in  cdt  with  loads  at  b  and  g,  multiply 


For  moment  at  ct  and  loads  at  b  and  g,  multiply 
wb  (=  wg)  by  panel  length  and  by  +  0.136. 


142 


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156 


TOP  CHORD  LOADED  TRANSVERSELY. 

To  proportion  chord  sections  which  are  subjected 
to  a  bending  load  in  addition  to  direct  compression  let 
M  =  the  bending  moment  in  inch  pounds, 
C  =  direct   compression  due  to  position  as  a  truss 

member, 

A  =  required  area  of  section, 
I  =  moment  of  inertia  of  section, 
d  =  distance    from    neutral    axis  to    extreme    top 

fibre;  then 

Q 

—  =  Direct  compression  per  square  inch, 

A. 

Mflf 

-  —  compression    per    square   inch   in    extreme 

fibre  due  to  bending. 

y  _  C  +  M^  =  resultant  fibre  6tress  .....  (j) 

A  1 

But  I  =  A  r2,  and  substituting  in  equation  (i), 

/=  —  +  M-4-  from  which 
A       AH 

_  C  r2  +  M  d 


If  the  specified  unit  stresses  for  bending,  live  and 
dead  loads  have  different  values,  then  let, 
ft  =  unit  stress  for  transverse  load, 
/i  =  unit  stress  for  live  load, 
/d  =  unit  stress  for  dead  load,  then 

M  d 
At  =  -f  —  j  ~  area  required  for  bending, 

Cl 
Al  =  -r-  =  area  required  for  live  load  stress, 

Ad=  7-  =  area  required  for  dead  load  stress, 
yd 

and  A  =  At  +  Ai  +  Ad  =total  area  required. 


157 


A 

A.                  E 

\  w 

r 

i 

^<^yxX^ 

PORTAL  BRACING. 

.a 

^X^<1> 

t 

i 

^^^                                ^^^te, 

Direct    stresses    and 

T 

bending  moments  due 

1 
I 

•*           c         * 

to  a  load  W  applied  at 
B;  assuming  the  reac- 

i 

Fig.  I. 

tions  at  C  and  D  to  be 

1 

equal  to  ^W,  and  as- 

1 

suming  that  the  mem- 

i 

^W 

^LL 

bers  AD  and    BC  are 

[ 

)         2              ( 

*      2 

free  to  rotate  at  C  and 

A 

B  W 

^*       \ 

^£ 

. 

i* 

^^^                           ^      -X11 

In  Fig.  i  AB  and  EF 

i 

-^^C^ 

are  struts  and  AF  and 

1    v 

t-^xxX*^  ^SN*SS^ 

i. 

^^^                                       ^^^. 

EB  tensions  members. 

*E 

In  Fig.  2  AB  and  EF 
are    tension    members 

1 
d 

Fig.2. 

and    AF    and    EB    are 

I 

struts. 

i 
I 

In  Fig.  3  all  mem- 

i__ 

W 

W 

bers  are  struts. 

[ 

32             ( 

^^^^^^  ^^ 

s        £• 

Let  a,  b,  c,  d  and  e 

A 

Kd->^c-*^d^ 

represent    the    length 
of    the   several    mem- 
bers   as   indicated    in 
Figs,  i,  2  and  3,  and 

F 

i- 

ly^    V1 

/  o           \ 
//             \ 

F 

let   the  +  sign  repre- 

\ 

sent     a      compressive 

i 

Fig.  3. 

stress    and  the  —  sign 

^ 

tensile  stress  :  then 

1 

r 

r*?       < 

r*2" 

158 


Fig.  i.     Stress  AB  =  +  W  (^  +  i  ) 


B  F  has  no  direct  stress,  but  B  F  C  and  AED  are 
both  subjected  to  bending  moments,  varying  uniform- 
ly from 

M  =  O  at  A,  B,  C  and  D  to  M  =  ^L?  at  F  and  E. 

Fig.  2.     Stress  AB  =  -  W  ^ 


BFC  =  -  W 


A  E  has  no  direct  stress,  but  AED  and  BFC  are 
both  subjected  to  bending  moments,  varying  uniform- 
ly from 

M  =  O  at  A,  B,  C  and  D  to 


Fig.  3.     Stress  BH  =  +  W  (~b  +  i  ) 


\&  ft 

Bending  moments  at  E  and  F  =  -^— 


159 


CAMBER. 

Theoretically  a  truss  should  have  just  sufficient 
camber  to  bring  the  joints  of  the  compression  chords  to 
a  true  square  bearing  when  the  truss  is  fully  loaded. 
The  most  perfect  way  of  accomplishing  this  is  to  calcu- 
late the  lengths  of  the  various  members  in  the  position 
they  are  expected  to  assume  when  the  truss  is  fully 
loaded;  then  calculate  the  stresses  in  the  web  members 
for  the  same  condition  of  loading;  calculate  the  elonga- 
tions of  the  various  tension  members  and  the  shortening 
of  the  compression  members  due  to  the  stresses  under 
full  load  and  the  actual  sections  used;  then  diminish  the 
lengths  of  the  tension  members  and  increase  the  lengths 
of  the  compression  members  by  these  amounts. 

While  this  method  accomplishes  the  desired  pur- 
pose, it  does  not  give  directly  the  amount  of  camber 
which  the  truss  will  assume  when  erected  and  unloaded. 
This,  however,  may  be  calculated  if  desired. 

A  shorter  method,  and  the  one  more  generally  used, 
is  as  follows: 

Assume  the  amount  of  camber  to  be  given  to  the 
truss;  that  is,  the  versed  sine  of  the  camber  curve  of  the 
chord;  then  assume  the  chords  to  be  arcs  of  concentric 
circles  and  the  posts  to  be  intercepts  of  radii.  Knowing 
the  length  of  bottom  chord  panel  and  the  depth  of  truss, 
the  length  of  top  chord  panel  and  the  length  of  diagonal 
members  may  be  readily  obtained. 

Let  c  —  camber  desired 
d  —  depth  of  truss 
/  =  length  of  span 
n  =  number  of  panels  in  truss 
i  —  increase  of  top  chord  panel    over    bottom 
chord  panel, 

all  values  being  expressed  in  inches  or  all  in  feet. 


1 60 


Then: 


In  all  ordinary  cases  4C2  is  small  in  comparison  with 
the  other  values  in  the  formula  and  may  be  neglected; 
the  formula  then  becomes 

Scd 
l-~fo 

in  which  ^may  be  expressed  in  inches,  d  and  /in  feet, 
and  the  value  i  will  be  in  inches. 

Having  now  the  length  of  top  and  bottom  chord 
panels  the  diagonal  may  be  computed  as  the  hypothe- 
nuse  of  a  right  angled  triangle  of  which  one  side  is  the 
depth  of  truss  and  the  other  a  mean  of  the  top  and  bot- 
tom chord  panel  lengths. 


161 


LENGTH  OF  FLANGE  PLATES,  PLATE  GIRDERS. 
I 


The  lengths  of  flange  plates  for  girders  with  par- 
allel flanges  may  be  readily  obtained  analytically,  as 
follows;  let 

al  =  area  of  first  flange  plate 

a2—  area  of  first  and  second  plate 
a,=  area  of  first,  second  and  third  plate 
at  =  total  area  of  flange 
xx  =  length  of  first  flange  plate 
x2=  length  of  second  flange  plate 
x3  =  length  of  third  flange  plate 
/  =  length  of  span. 
From  the  equation  of  the  parabola 

(I'd    '  a±  '  '  x  2  •  x  2  •  I2 
**i  •  **2      t  •       i  •     2  • 

but  alt  a2,  at  an(j  /  being  known 


£*»*£«*.=/   121 


These  values  of  xlt  x2,  and  x3  may  all  be  obtained 
by  one  setting  of  the  slide  rule,  as  follows: 


Set  at  on  the  slide  to 


/  on  scale  of  squares;  then 

opposite  al ,  a2  and  a   on  the  slide  read  xx ,  xa  and 
on  the  scale  of  squares. 


162 


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167 


SAFE  WORKING  STRESSES  PER  SQ.  IN.  FOR  TIMBER. 

Denoted  by  S  in  Formula  for  Timber  Columns. 

Class 

For 
Typical  Species     Transverse 
Loading 

For  End 
Bearing 

For  Short 
Columns 
when 
/  <\ld 

For           For 

m?  S"? 

i 

White  Oak                 1400 

1300 

1000 

550              300 

2 

Long  Leaf  Pine          1600 

1300 

1000 

350               200 

3 

Whi»e  Pine                 1100 

900 

700 

200               150 

4 

Hemlock                      950 

850 

650 

200               100 

TIMBER   COLUMNS. 

Table  giving  values  of  factor  L 

,|     | 

in  Column  Formula  F  —  S  - 

1 

n  /' 

1  1000  fl?2                                             *  '   luuOrfs 

F 
S 

=  Safe  load  per  sq.  in.  for  column  of  length  /. 
=     "       "      "     "     "   for  short  column,  taken  from  table  above. 

d 

=  Length  of  column,  in  inches. 
=  Least  side  of  column,  in  inches. 

Length 

LEAST  SIDE  OP  COLUMN  IN  INCHES  =  d 

of  Column 

8 

in  Feet 

4 

5 

6 

7 

9 

10 

11 

12 

13 

14 

15 

16 

4 



3T 

3 

.75 

.82 

.87 

.90 

___ 

3 

.63 

.73 

.79 

.85 

7 

.89 

>--— 

___ 

10 

.52 

.63 

.71 

.78 

.80 

.84 

.87 

.89 

_.  „.  _ 



1 

2 

43 

54 

63 

70 

7 

S 

79 

.82 

.85 

.87 

.89 

14 

,46 

,56 

.63 

.69 

.74 

.77 

.81 

.83 

.85 

.87 

.88 

16 

.49 

.57 

.63 

.68 

.73 

.76 

.79 

.81 

.84 

.86 

.87 

1 

3 

,43 

,51 

,5 

7 

.63 

.68 

.72 

.75 

.78 

.81 

.83 

.85 

2 

3 

46 

,5 

?, 

,59 

.63 

.67 

.71 

.74 

.77 

.79 

.82 

22 

.41 

.47 

,53 

.58 

.63 

.67 

.70 

.74 

.76 

.78 

2 

| 

1 

,4 

3 

.49 

.54 

.59 

.63 

.67 

.70 

.73 

.76 

2 

45 

,50 

,55 

,59 

.63 

.67 

.69 

.72 

28 

.46 

.51 

.56 

.60 

.63 

.67 

.69 

3 

1 

,42 

.48 

,52 

.57 

.60 

.63 

.66 

32 

.45 

.49 

.53 

.57 

.60 

.63 

3 

t 

""" 

.46 

.50 

.54 

.57 

.61 

36 

.43 

.47 

.51 

.55 

.58 

3 

3 

uim™* 

.44 

.49 

.52 

.55 

40 

.42 

.46 

.49 

.53 

4 

I 

— 

.44 

.47 

.50 

44 

—  — 

.45 

.47 

4 

.43 

.46 

48 

.44 

1 68 


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169 


COOPER'S    STANDARD   LOADING 

FOR   RAILROAD   BRIDGES. 

S-rs 

J4d 

i-^ 

5_it 

{3 

iS  * 

J*~ 

it 

Jl 

^  s. 

10 
IO 

CD 
10 

Q 

10 

10 

s  • 

g  • 

fc 

(0         CO 

M 

u 

§  • 

«        0 

Q 

10 

a 

10 

10 

m 

CO 

32500 
32500 
32500 
32500 

500CO 
50000 
50000 
50000 

25000 

325CO 
32500 
32500 
32500 

50000 
50000 
50000 
50000 

25000 

29250 
29250 
29250 
29250 

450CO 
45000 
45000 
45000 

22500 

29250 
2S250 
29250 
29250 

45000 
45COO 
4EOCO 
45000 

22500 

26000 
26000 
26000 
26000 

40000 
40000 
40000 
40000 

20000 

26000 
26000 
26000 
26000 

40000 
40000 
40000 
40000 

20000 

19500 
19500 
19500 
19500 

30000 
30000 
30000 
30000 

15000 

19500 
19500 
195CO 
19500 

30000 
30000 
30000 
30000 

15000 

• 

>< 

y 

w 

€i 

• 
ei 

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Class 

E50 

E45 

141 

III 

E 

170 


THE  OSBORN  ENGINEERING  COMPANY'S  STANDARD  LOADING 
FOR  ELECTRIC  RAILWAY  BRIDGES. 


5'6" 


16'  o 


16'  o" 


5' 6"    7'c"      5' 6" 
LIVE  LOAD  "A." 

Train  of  74-ton  Coal  Cars. 

Weight  of  Car  =    38,000  Ibs. 

Rated  Capacity  =  100,000    ' 

10%  Overload  =    10,000    " 

Total  Load  =  148,000    " 

Axle     "  =    37,000    " 


J                II                1 

r 

)( 

3                  G 

)( 

)     ( 

)( 

*\                 r 

L)  (, 

2 

5  o  19  o  50      8 

LIVE  LOAD  "B." 

Train  of  62-ton  Coal  Cars. 

Weight  of  Car  =    36,000  Ibs. 
Rated  Capacity  =   80,000  " 
10%  Overload  =     8,000  " 
Total  Load         =  124,000   " 
Axle    "  =   31,000  " 


LIVE  LOAD  "C." 

Train  of  46-ton  Flat  Cars — Same  wheel 
spacing  as  for  62-ton  Coal  Cars. 

Weight  of  Car   =  26,000  Ibs. 
Rated  Capacity  =  60,000  " 
10  %  Overload    =    6,000  " 


Total  Load 
Axle 


=  92,000 
=  23,000 


£ 

\    I 

)                      C 

)    < 

^               C 

)    ( 

1                      C 

)    ( 

1 

6'o*  i6'o"         6'o"       12' of       6'o"  l6'o"         6' o" 

LIVE  LOAD  "D." 

Train  of  4O-ton   Motors. 

Axle  Load  =  20,000  Ibs. 

NOTE. — Live  Load  "A"  should  be  used  for  roads  designed  for  heavy  coal  traffic,  etc. 

Live  Losd  "B"        "         "  "  "      to  carry  occasional  coal  cars. 

Live  Load  "C"  "  "  "  "  "  "  ordinary  freight  traffic, 

but  not  cars  of  over  60,000  Ibs  capacity  This  excludes  coal  traffic. 

Live  Load  "D"  should  be  used  for  roads  designed  for  passenger  and  ex- 
press traffic  only 


171 


THE  OSBORN   ENGINEERING  COMPANY'S 
STANDARD  LIVE  LOADS  FOR  HIGHWAY  BRIDGES. 


UNIFORM  UVE  lyOADS 

For  country  bridges  carrying  heavy  traffic,  and  for  city  bridges : 
for  spans  up  to  150  feet  long,  100  Ibs.  per  square  foot  of  roadway  and 
80  Ibs.  per  square  foot  of  sidewalks.  For  spans  over  150  feet  long, 
80  Ibs.  per  square  foot  of  both  roadway  and  sidewalks. 

For  country  bridges  carrying  ordinary  or  very  light  traffic:  for 
spans  up  to  150  feet  long,  80  Ibs.  per  square  foot  of  both  roadway 
and  sidewalks.  For  spans  over  150  feet  long,  60  Ibs.  per  square  foot 
of  both  roadway  and  sidewalks. 

CONCENTRATED  UVE  I,OADS. 

For  country  bridges  carrying  heavy  traffic,  and  for  city  bridges: 
a  steam  road  roller  weighing  35,000  Ibs.,  arranged  as  follows:  15  ooo 
Ibs.  on  forward  roll  and  10,000  Ibs.  on  each  rear  roll;  axles  eleven 
feet  apart,  forward  roll  four  feet  face,  rear  rolls  each  twenty  inches 
face,  rear  rolls  five  feet  center  to  center. 

For  country  bridges  carrying  ordinary  traffic:  a  steam  road 
•roller  weighing  21,000  Ibs.,  arranged  as  follows:  9,000  Ibs.  on  for- 
ward roll  and  6,000  Ibs.  on  each  rear  roll;  axles  eleven  feet  apart, 
forward  roll  four  feet  face,  rear  rolls  each  twenty  inches  face,  rear 
rolls  five  feet  center  to  center. 

For  country  bridges  carrying  very  light  traffic:  a  single  horse 
roller  weighing  12,000  Ibs.,  the  roll  five  feet  face;  or  a  wagon  load 
of  io,ooq  Ibs.  on  two  axles  eight  feet  apart,  wheels  five  feet  gauge. 

Unit  stresses  may  be  increased  twenty-five  per  cent,  for  the  road 
rollers,  but  concentrated  loads  should  not  be  considered  as  distrib- 
uted over  two  or  more  stringers,  except  when  such  distribution  un- 
questionably occurs. 

If  a  paved  floor  of  sufficient  width  be  used,  the  rollers  should  be 
considered  when  turned  at  right  angles  to  the  axis  of  the  bridge. 

If  the  structure  is  to  be  designed  for  the  present  or  future  ac- 
commodation of  electric  railways,  suitable  concentrations  should 
be  selected  from  page  171,  and  the  structure  proportioned  for  these 
concentrations  also. 


172 


IMPACT   FORMULAE. 


THEOSBORN  ENGINEERING  CO. 


where  I  «•  Impact. 

"L,  =  Maximum  live  load 

stress. 
D  =  Dead  load  stress. 


THE  AMERICAN  BRIDGE  CO. 


-      L  +  300 
Where  I  =*  Impact. 

S  =  Maximum  live  load 
stress. 

1.  =  length  in  feet  of 
loaded  distance  which  produces 
maximum  stress  in  member. 


THE  OSBORN  ENGINEERING  COMPANY'S 
STANDARD  UNIT  STRESSES 


Pounds  per  Square  Inch 


NATURE  OF  STRESS 

For 
Railroad 
Bridges 

For 
Electric 
Railway 
Bridges 

For 
Highway 
Bridges 

TENSION 

Wrought  Iron, 

13,000 

15,000 

18,000 

Soft  Steel, 

15,000 

17,000 

20,000 

Medium  Steel, 

17,000 

19,000 

22,000 

COMPRESSION 

Values  of  C  in  formulae  at  bottom 

of  page, 

Wrought  Iron, 

13,000 

15,000 

18,000 

Soft  Steel, 

15,000 

17,000 

20,000 

Medium  Steel, 

17,000 

19,000 

22.000 

Values  of  ~  in  the  formulae  below 

should  not  exceed: 

for  main  members, 

100 

100 

125 

for  subordinate  members, 

120 

120 

150 

BENDING 

Pins,  closely  packed,  medium  steel, 

25,000 

25,000 

25,000 

BEARING 

Pins,                              medium  steel, 

22,000 

24,000 

24,000 

Rivets,                         rivet  steel, 

20,000 

22,000 

22,000 

SHEARING 

Pins,                              medium  steel, 

11,000 

12,000 

12,000 

Rivets,                            rivet  steel, 

10,000 

11,000 

11,000 

Webs  of  plate  girders,  soft  steel, 
"              "           "      medium  steel, 

9,000 
10,000 

10,000 
11,000 

10,000 
11,000 

COMPRESSION  FORMULAE: 
Square  Bearing. 

12500 


Soft  Steel,    8  = 


Pin  and  Square  Bearing 

12500 


1  + 


1  + 


/2 


Medium  Steel,  S  = 


15000 


24000 r2 
15000 


36000  r* 


18000  r2 


S=  Working  strength  in  Ibs.  per  sq.  in.;     /=  length  in  inches  ; 
r  =  least  radius  of  gyration  in  inches. 


173 


VALUES  OF  MOMENTS  OF  INERTIA  FOR  STANDARD  SHAPES 
OF  THE  CARNEGIE  STEEL  COMPANY. 


I = Moment  of  Inertia  neutral  axis  parallel  to  flange. 
I/=     «          »       "  "         -  ««         "   web. 


j  Area— A=dt-f-(s-}-y)2z. 


— I4)]. 


Area=A-dt+(s+y)z. 


—  t*)]-Ax2. 


1 


—  8c(h— ^)3]. 
I'=TV[d(b4-c)3— 2hc3— 6hcb2]. 


"T 1 


— t)t. 


2(h+b) 
l-x)»-(b-t)(x-t)»]. 


174 


VALUES  OF  I  (Moment  of  Inertia)  AND  S  (Section  Modulus) 
FOR  USUAL  SECTIONS. 


bh3 

~"  12  ' 


bh3 
"36' 


bh2 


bh2 
—  . 


12 


=0.0491  d4. 


32 

=0.0982  d 


-"--A'A 


1= 


1=0.0491 


I_b/n3+bn/3-(b-b/)a3 
_____          _ 


0.0982  (d3-— 


Min.= — . 

n 


I=- 


bh3-2b'b/3 

12 


x  x  Denotes  position  of  neutral  axis. 


175 


CONVENTIONAL   SIGNS  FOR  BRIDGE  RIVETS. 

Shop.         Field. 
Two  Full  Heads. 


Countersunk  Inside  and 
Chipped. 


Countersunk  Outside  and 
Chipped. 

Countersunk  Both  Sides  and 
Chipped. 


Inside.       Outside.   Both  Sides. 


(DO® 


ODOqp 


Flattened  to  y%"  high  or 

Countersunk  and  not 

Chipped. 


Flattened  to 


Flattened  to 


The  foundation  of  the  above  system  is  the  diagonal  cross  to 
represent  a  countersink,  the  blackened  circle  for  a  field  rivet,  and 
the  verticle  stroke  to  indicate  a  flattened  head.  The  position  of  the 
cross  with  respect  to  the  circle  (inside,  outside  or  both  sides)  indi- 
cates the  location  of  the  countersink,  and  the  number  and  position 
of  the  verticle  strokes  indicate  the  height  and  position  of  the  flat- 
tened heads. 

Any  combination  of  field,  countersunk  and  flattened  head  rivets 
liable  to  occur  may  be  readily  indicated  by  the  proper  combination 
of  the  above  signs. 


176 


BRIDGES. 


SOME  HISTORICAL  AND  OTHER  INTERESTING  DATA. 

HISTORICAL. 

Ancient  bridges  are  known  to  have  existed  in  China,  Assyria 
and  India  long  before  the  Christian  Eta.  Stone  bridges,  built  of 
slabs  on  piers,  were  built  by  the  Greeks. 

The  origin  of  the  arch  may  be  traced  back  to  the  Chaldeans  and 
Assyrians.  Crude  arches  of  brick  have  been  found  in  ruins  of 
Thebes,  probably  built  about  2900  B.  C.  The  Romans,  however, 
were  probably  the  first  to  use  the  arch  understandingly,  about  the 
second  century  B.  C. 

The  first  bridge  in  the  United  States,  so  far  as  known,  was  a 
pile  trestle,  built  in  1660,  across  Charles  River,  near  Boston. 

A  noted  long  wooden  span  was  the  bridge  "Colossus."  340'  3%" 
long,  built  by  lyouis  Wernwag  ,  about  1812,  at  Philadelphia,  on  the 
site  of  the  present  Callowhill  bridge. 

The  first  iron  bridge  in  the  world  was  built  over  the  Severn 
River  at  Ironbridge,  England,  in  1779.  It  was  a  cast  iron  arch  of 
100'  6"  span  and  40'  rise.  The  next  was  the  "Buildwas  Bridge,"  a 
similar  structure,  built  over  the  same  river  by  Telford  in  1796;  span 
130',  rise  17'. 

The  firs,t  iron  railway  bridge  was  built  in  1823,  for  the  Stockton 
and  Darlington  Railway,  over  the  Gaundless  River,  a  tributary  of 
the  Wear  River,  in  England,  a  cast  iron  trestle  consisting  of  four 
spans  i  a'  6"  each. 

The  first  plate  girders  were  made  in  England  in  1846,  by  Fair- 
bairn,  from  designs  by  Stephenson.  They  had  cast  iron  flanges. 

The  first  bridge  across  the  Mississippi  River  was  a  suspension 
bridge,  built  1855,  at  Minneapolis,  620'  span.  There  are  now  forty- 
six  bridges  across  that  river. 

Suspension  bridges  are  said  to  have  been  built  in  China  over 
2000  years  ago.  Such  structures  were  built  in  Europe  as  early  as 
1615. 

The  first  chain  bridge  in  England  was  a  foot  bridge  of  70'  span 
built  about  1741,  over  Tees  River. 

The  first  chain  bridge  in  the  United  States  was  built  by  Finlay, 
in  1796,  over  Jacob's  Creek,  near  Uniontown,  Pa.  The  first  wire 
suspension  bridge  in  the  United  States  was  built  in  1816,  over  the 
Schuylkill  River,  in  Philadelphia. 


177 


The  first  suspension  bridge  over  the  Niagara  River  was  built 
by  Charles  Kllet,  in  1848.  The  only  railway  suspension  bridge  in 
the  world  was  built  by  Roebling  at  Niagara,  in  1855. 

Wooden  cantilever  bridges  were  built  by  the  Assyrians  as  early 
as  2000  B.  C. 

The  first  cantilever  bridge  of  importance  to  be  built  in  the 
United  States  was  the  Kentucky  River  Bridge,  built  by  C.  Shaler 
Smith,  in  1877.  Total  length,  1125';  being  three  equal  spans  of  375'. 
The  second  was  the  Minnehaha  Bridge  over  the  Mississippi  River 
at  St.  Paul,  built  in  1880,  with  center  span  of  324'.  The  third  was 
the  Niagara  cantilever,  built  in  1883,  with  center  span  of  420'. 

The  Romans  built  cement  arches ;  remains  of  them  still  exist. 
Since  their  times  the  earliest  was  a  concrete  arch  of  31'  span,  built 
by  John  C.  Goodrich  in  1871,  in  Prospect  Park,  Brooklyn,  known  as 
the  Cleftridge  Bridge. 

Reinforced  concrete  was  first  used  by  Monier  in  1876. 

The  first  reinforced  concrete  bridge  in  the  United  States  was 
built  according  to  the  Ransome  system,  in  1889,  at  Golden  Gate 
Park,  San  Francisco.  Span  20'. 

EVOLUTION  OF  TYPES  IN  THE  UNITED  STATES. 

The  first  known  patent  for  a  bridge  was  granted  to  Chas.  W. 
Prale,  Jan.  2,  1797. 

Patents  were  also  granted  to  Timothy  Palmer,  Dec.  17,  1797  • 
to  Thomas  Pope,  April  18,  1807 ;  to  lyouis  Wernwag,  and  several 
others;  but  the  Patent  Office  records  were  burned  in  1836  and  could 
not  be  restored. 

The  first  patent  for  a  truss  bridge  was  granted  to  Theodore 
Burr,  in  1817.  The  designs  consisted  of  trusses  reinforced  with 
wood  arches. 

Three  noted  names  connected  with  early  bridge  building  in  the 
United  States  are  Theodore  Burr,  Timothy  Palmer  and  I,ouis 
Wernwag. 

Ithiel  Towne  patented  the  lattice  girder  bridge  in  1820. 

I^ong  patented  his  types  in  1830  and  1839. 

The  first  iron  truss  bridge  was  patented  in  1833,  by  Augustus 
Canfield.  The  first  one  built  was  over  the  Erie  Canal  at  Frankfort, 
N.  Y.,  in  1840,  by  Earl  Trumbull.  It  was  a  combination  of  cast 
iron  segments  and  suspension  rods,  with  an  anchored  top  chord  in 
tension. 

Wm.  Howe  patented  his  type  in  1840. 

Squire  Whipple  built  his  first  bridge  in  1840.  It  was  a  bow- 
string truss  with  cast  iron  compression  members  and  wrought  iron 
tension  members.  He  secured  a  patent  on  the  type  April  24,  1841. 


178 


Thos.  W.  and  Caleb  Pratt  patented  the  Pratt  truss  April  4,  1841. 

Wendell  Bollman's  first  bridge  was  built  over  the  Potomac 
River  at  Harper's  Ferry,  in  1852.  It  was  a  124'  span. 

Albert  Tfink  built  a  three  span  bridge  over  the  Monongahela 
River  in  1852. 

The  first  pin  connected  span  was  built  by  John  W.  Murphy  in 
1859,  over  a  canal  at  Phillipsburg,  N.  J.  It  was  a  165'  span  and  was 
called  a  "Whipple-Murphy"  bridge. 

The  first  bridge  in  which  wrought  iron  was  used  for  both 
tension  and  compression  members  was  built  by  Murphy  over  the 
I«ehigh  River,  at  Mauchchunk,  for  the  I^ehigh  Valley  R.  R. 

The  first  riveted  lattice  girders  were  built  in  1859  for  the  New 
York  Central  R.  R.,  by  Howard  Carroll. 

S.  S.  Post  built  the  first  bridge  of  his  type  in  1865,  for  the  Erie 
R.  R.,  at  Washingtonville. 

In  1874,  James  B.  Hades  built  the  Mississippi  River  Bridge  at  St. 
L,ouis.  It  consists  of  three  trussed  arches,  one  of  520'  and  two  of 
502'  span. 

THE  LONGEST  BRIDGE  STRUCTURES. 

Congest  wooden  structure — a  pile  trestle  across  I«ake  Pontchar- 
train,  near  New  Orleans,  l,a.,  21  miles  long. 

Congest  metal  structure— the  Tay  Viaduct,  Scotland,  10,800  feet 
long,  iron  lattice  girders.  The  bridge  across  the  St.  I^awrence 
River  at  Montreal  has  a  total  length  of  8,791  feet. 

Longest  masonry  structure— the  I^ion  Bridge  in  China,  across 
an  arm  of  the  Yellow  Sea,  22,968  feet  long,  composed  of  300  arches. 


THE  HIGHEST  BRIDGE  STRUCTURES. 


Name 

Country 

Length, 
Feet 

Height, 
Feet 

St.  Giustina 

Switzerland 

197 

460 

Garabit 

France 

1852 

406 

Du  Viaur 

France 

1508 

382 

Stoney  Creek 

British  Columbia 

336 

340 

Loa 

Bolivia 

800 

336 

Pecos  River 

United  States 

2180 

328 

Gokteik 

Burmah 

2260 

320 

Kinzna 

United  States 

2052 

302 

179 


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